KANSAS CITY, Mo. — The New England Patriots had played the lack-of-respect card. Quarterback Tom Brady had declared publicly that everyone thought they stunk, to paraphrase it kindly, and couldn’t win any games. They had to take their dynasty, which hasn’t always traveled so well at this time of the year, on the road.

But they are still the Patriots. And now the Patriots are back where they almost always show they belong. They advanced to yet another Super Bowl by outlasting the top-seeded Kansas City Chiefs, 37-31, in overtime Sunday evening in the AFC championship game.

“The odds were stacked against us,” Brady said Sunday night. “And it hasn’t been that way for us for a while. It certainly was for us this year. We started off so slow. . . . The last four games have been our best games.”

The Patriots will meet the Los Angeles Rams on Feb. 3 in Atlanta in their ninth Super Bowl appearance with Brady as their quarterback and Bill Belichick as their coach. They will be seeking their sixth Super Bowl triumph in that span.

“A victory on the road [in the] AFC championship game is one of my sweeter victories, definitely, in my career,” Patriots tight end Rob Gronkowski said.

Running back Rex Burkhead’s two-yard touchdown run 4:52 into overtime won it for the Patriots. That came after they quieted the NFL’s highest-scoring offense and kept the league’s likely MVP in check for a half, then traded touchdowns with the Chiefs and their magnificent second-year quarterback, Patrick Mahomes, down the stretch.

“I think when you’ve got 70,000 people cheering against you, it’s pretty sweet when you win on the road,” Brady said. “And it’s a hard thing to do in the NFL. It’s certainly a hard thing to do against the first-ranked team in the conference who’s been playing great all year and certainly played well at home. We knew it was going to take a lot.”

Postseason victories on the road have been scarce for the Patriots. They entered this game 3-4 in playoff games on the road with Belichick and Brady and didn’t have a postseason victory away from home since 2007.

Their performance Sunday wasn’t flawless. Brady threw two interceptions. Wide receiver Julian Edelman came close to muffing a punt but was saved by an instant replay review that overturned a Chiefs recovery, and he had a Brady pass clank off his hands for an interception.

But the Patriots were good enough. They controlled the first half. They had leads of 14-0 at halftime and 17-7 into the fourth quarter. They fell behind 21-17 on Mahomes’s third touchdown pass of the game. The Patriots reclaimed the lead with a little more than 31/2 minutes to play in regulation on a 10-yard touchdown run by running back Sony Michel on a fourth-and-one play. The Chiefs moved in front 28-24 on a touchdown run by Damien Williams with 2:03 remaining.

Burkhead’s four-yard touchdown gave the Patriots the lead again with 39 seconds to go. The Chiefs forced overtime with a 39-yard field goal by kicker Harrison Butker with eight seconds left. But the Patriots got the ball first in overtime and drove, virtually unimpeded, to the winning touchdown.

“We just knew we had to go down and score,” Gronkowski said of the overtime possession. “We were saying on the sideline: ‘Let’s just go down and end this now. Let’s make some plays. Everyone step up.’ ”

That’s precisely what the Patriots did in denying the Chiefs a Super Bowl trip.

“You’re doing everything you can to get to the Super Bowl and to win it,” Mahomes said. “And for this opportunity to fall short, I mean, it’s going to hurt. . . . You have to go through that. But at the same time, when you come back and look at the bigger picture, you know that you can build off this and use this feeling as motivation to come back and win next time.”

The Chiefs had never been shut out in the first half of a home game with Andy Reid as their coach — until Sunday. The Patriots were dominant in the half, taking a 14-0 lead while holding the ball for more than 21 minutes and outgaining the Chiefs 245 yards to 32.

Michel had an opening-drive touchdown run, and Brady threw a touchdown pass to wide receiver Phillip Dorsett in the final minute of the half. The lead could have been bigger if Brady had not thrown an end zone interception earlier in the second quarter. But Mahomes was off his game, overthrowing Williams when the running back was wide open for what should have been a second-quarter touchdown.

Mahomes got moving in the second half. He threw a third-quarter touchdown pass to tight end Travis Kelce. The Chiefs rolled to 24 fourth-quarter points. But the Patriots remained the Patriots, and they are headed to the Super Bowl for a third straight season and for the fourth time in five years.

“It’s a great feeling,” Brady said. “We’ve overcome a lot this year, down but not out. We found a way to play our best the last four games. . . . We’re going to need one more great game. Great way to end it. That was probably as excited as I’ve been in a long time.”

-- Mark Maske

Key plays:

Patriots win: It would be unfair to say that the biggest play in overtime was New England’s Matthew Slater calling the coin flip correctly, thus giving his team the ball, because Tom Brady converted three third-and-10 plays on the ensuing drive, which ended with Rex Burkhead reaching the end zone on a two-yard run, giving his team a 37-31. 15-play drive 80 yards. (New England, 37-31, overtime).

Thus the Chiefs, who had the NFL’s highest-scoring offense in the regular season and were coming off a 24-point fourth quarter, never got the chance to have the ball in overtime, and they could only watch as New England celebrated yet another AFC title and Super Bowl berth on their home turf in Kansas City.

To overtime we go: After getting the ball back with just 39 seconds left, the Chiefs managed to get into field goal range, at which point Harrison Butker came through on a 39-yard attempt with eight seconds left in regulation. Four play, 48-yard drive. (Tie game, 31-31, 0:08, fourth quarter)

The Patriots let the rest of the clock run out to go to overtime, meaning that both conference title games went to an extra session. Exciting enough for ya?!

Costly penalty: Oh, what a bad penalty by Dee Ford. The Kansas City defensive end lined up in the neutral zone, incurring a five-yard penalty that negated a Tom Brady interception that would have sealed a win for the Chiefs. Instead, the Patriots moved on to score a touchdown on a four-yard Rex Burkhead rush, leading to a 31-28 lead with 39 seconds left. Six-play drive, 65 yards. (New England, 31-28, 0:39, fourth quarter)

Chiefs lead again: What a fourth quarter! Kansas City stormed back for the third lead change of the frame, with Damien Williams running it in from two yards out for his third touchdown of the quarter. The big plays were a pass interference flag on the Patriots for a 23-yard gain, followed by a 38-yard completion from quarterback Patrick Mahomes to wide receiver Sammy Watkins. But did the Chiefs leave too much time on the clock? Five-play, 68-yard drive (Kansas City, 28-24, 2:04, fourth quarter).

Patriots answer: New England, as it is wont to do, refused to wilt and came right back down the field for a touchdown that helped it retake the lead, 24-21. Sony Michel rushed 10 yards for the score, but the story of the drive, to many observers, were the calls that went New England’s way, including a very iffy roughing-the-passer flag and a ruling of a catch that was upheld, although replays showed that wide receiver Chris Hogan might have let the ball hit the turf.

Chiefs take the lead: From 14-0 down, the Chiefs have stormed back to take a 21-17 lead. Kansas City took full advantage of Tom Brady’s second interception, getting to the end zone on a 23-yard screen pass from Patrick Mahomes to running back Damien Williams. The two-play drive took 23 yards. (Kansas City, 21-17, 7:45, fourth quarter)

Huge sequence: The Patriots' Julian Edelman was ruled to have fumbled a punt, with the Chiefs recovering the ball for a massive turnover at New England’s 27. However, video replays indicated that the ball might have taken an odd hop off the turf just before Edelman attempted to grab it, and that it may have just barely bounced past him without any contact. That was what officials ruled after further review, and the Patriots kept possession.

Depending on how the game turns out, this may go down as a crucial officiating moment, albeit one not likely to raise quite the same outcry as the non-call on a would-be pass interference toward the end of regulation in the NFC championship.

But wait! As Tony Romo said it on CBS’s telecast, “The ball doesn’t lie.” Two plays after the non-turnover, Edelman let a Tom Brady pass bounce off his hands for a Chiefs interception.

Stuffed: The Chiefs' defense came though in a huge spot, denying the Patriots on a fourth-and-1 play from the Kansas City 25. Tom Brady eschewed a potential quarterback sneak, instead turning and handing the ball to running back Rex Burkhead, but he was stopped cold for no gain. Thus the Chiefs got the ball back while still down by three points, 17-14.

Chiefs score: The third quarter ended with the Chiefs down by 10 points but having driven well into Patriots territory, facing a second-and-10 play at New England’s 14. Two plays later, Kansas City was in the end zone, thanks to a one-yard pass from Patrick Mahomes to running back Damien Williams.

On the previous play, the first of the fourth quarter, the Patriots were called for pass interference on tight end Travis Kelce in the end zone, giving the Chiefs the ball at the goal line. Mahomes cashed in from there, finishing off a nine-play, 75-yard drive. (New England, 17-14, 14:51, fourth quarter).

The kick is good: The Patriots bumped their lead back up to 17-7 on a 47-yard field goal by Stephen Gostkowski. New England had gotten the ball in excellent field position, at the Chiefs' 37-yard line following a poor punt, so Kansas City could be reasonably satisfied in limiting the damage, but the team’s comeback just got a bit harder. It was a six-play, eight-yard scoring drive. (New England, 17-7, 4:07, third quarter)

Another no-look?: After the Chiefs forced a Patriots punt, Patrick Mahomes went back to work, but Travis Kelce dropped a pass that might have gone for a first down. The pass appeared to feature another no-look move by the quarterback, or at least a version thereof, but the drive ended with Kansas City having to punt the ball away.

Quick strike: The Chiefs did exactly what they had to do to start the second half: score, and score quickly. Patrick Mahomes completed a 54-yard pass to wide receiver Sammy Watkins and followed it up immediately with a 12-yard scoring toss to tight end Travis Kelce, and Kansas City cut New England’s lead to 14-7. The score capped a four-play, 74-yard drive (New England, 14-7, 12:56, third quarter).

Up at the half: After Patrick Mahomes was sacked, and he fell on his own fumble to avert further disaster for Kansas City, the first half ended with the Patriots leading, 14-0.

Last-minute score: The Patriots scored a second touchdown on a 29-yard touchdown pass from Tok Brady to wide receiver Phillip Dorsett. That gave New England a 14-0 lead just before halftime, after an eight-play, 90-yard drive (New England, 14-0, 0:27 second quarter).

Missed opportunity: We finally saw some of that Patrick Mahomes magic, but the Chiefs quarterback ended up badly missing on what would have been a wide-open touchdown. Two plays later Mahomes took a sack that took Kansas City out of field goal range, and his team was forced to punt the ball back to the Patriots, still down 7-0.

On that drive, Mahomes had escaped pressure on a third-down play by rolling to his left, then throwing across his body to wide receiver Sammy Watkins for a 12-yard gain. Mahomes followed that up with a 42-yard strike to wide receiver Tyreek Hill, but the next play found the 23-year-old quarterback overthrowing running back Damien Williams on a wheel route that had Chiefs tight end Travis Kelce raising his arms in anticipation of a score that was not to be.

Chiefs need to get going: Kansas City was finally able to force the Patriots to punt, albeit only after New England incurred a delay of game on a fourth-and-1 play on the Chiefs' 42-yard line. Even though Kansas City is still only down 7-0, it desperately needs to get something going on offense.

At the start of their third drive, the Chiefs had only run eight total plays for a total of minus-two yards. Patrick Mahomes, who threw for 50 touchdowns and over 5,000 yards in the regular season and is the front-runner for NFL MVP honors, had been completely held in check.

Major mistake: The first quarter ended with the Patriots very well-positioned to add to their 7-0 lead, but Tom Brady threw an interception in the end zone on a third-and-goal play from the 1-yard line, keeping the Chiefs from falling any further behind. Linebacker Reggie Ragland made the play for Kansas City, and he stayed in the end zone for a touchback.

Before that momentum-altering moment, New England’s second drive had picked up right where the first left off, except it began in better field position after a sack forced Kansas City to punt from near its own end zone. On the ensuing Patriots possession, they were able to keep running effectively and picking up first downs, with running back James White, usually a receiving threat, converting third downs with his legs.

Strong start on the road: The Patriots enjoyed an ideal start to the AFC championship, grinding down the Chiefs with a meat-and-potatoes, chain-moving drive that took over eight minutes off the clock and resulted in a 7-0 lead. Running back Sony Michel carried seven times for 32 yards and a touchdown, while quarterback Tom Brady threw his trademark assortment of short, well-aimed passes, as New England kept Kansas City’s high-powered offense waiting in the cold to take its turn.

The Chiefs had won the coin toss and elected to defer, giving New England the ball first. Kansas City will thus get the ball to start the second half, but it may already be regretting the decision to let the Patriots draw first blood. The drive went 80 yards on 15 plays (New England, 7-0, 6:55, 1st quarter).

Rams await: The football world awaits its AFC champion, but we know who is waiting to play either the Patriots or Chiefs in the Super Bowl: the Rams. Los Angeles overcame an early, 13-0 deficit, plus deafening roars from Saints fans at New Orleans’s domed stadium, to scratch out a win in overtime, 26-23.

The victory was marred, certainly in the eyes of Saints fans, by some questionable officiating, particularly a no-call on what appeared to be a pass interference penalty committed by the Rams that would have given New Orleans a chip-shot field goal attempt to win the game with seconds left in regulation. However, Los Angeles fans could point to other decisions along the way that went against their squad, and with the first possession in the extra session, the Saints had a chance to win it with a touchdown drive. — Des Bieler

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