Patriots tight end Rob Gronkowski catches a touchdown pass with Tennessee Titans safety Kevin Byard (31) defending during the second half of Saturday night’s game in Foxborough, Mass. (Steven Senne/Associated Press)

A cold wind blew Saturday night into Gillette Stadium, and it could have been taken for either foreboding chill or frigid comfort. Palace intrigue swirled all week around the New England Patriots, a foreign commotion for the NFL’s crown jewel franchise. But the Patriots have not won five Super Bowls without meeting disruption and smashing it into powder. Nothing could soothe their turmoil, whatever amount existed, like January football in a Massachusetts freeze.

If the Patriots really are a dynasty on the brink of downfall, they are an active dynasty nonetheless, still lording over the league with metronomic virtuosity. If the Patriots are squabbling, it did not prevent their advancement to a seventh consecutive AFC championship game, the prize for their 35-14 demolition of the game-yet-helpless Tennessee Titans.

Pause and think about that for a second: Every year since “Game of Thrones” made its television debut, the Patriots have stood among the final four NFL teams. The last time the Patriots did not make the AFC title game was 2010 — Mike Shanahan’s first season with the Redskins, the year before Jim Harbaugh took over the 49ers and Sam Bradford’s rookie season.

“This team has always been consistent in what they did, and they always stick to what they know, and that’s winning,” said defensive lineman Ricky Jean-Francois, a late-season addition. “Besides winning, they stuck to the process. They stick to the journey. They stick to the grind — everything that leads to a game like this.”

The Titans, two-touchdown underdogs, put a brief scare into the Patriots, taking a 7-0 lead late in the first quarter. New England scored the next 35 points as Tom Brady choked the life out of another opponent on another January Saturday night in Foxborough. He surpassed 300 yards passing in a playoff game for the 13th time, making every throw imaginable and some outside those bounds, submitting a classic performance in his first as a quadragenarian.

Brady overcame a lack of separation from his outside receivers and shredded the Titans with short, precise passes. He completed 35 of 53 passes for 337 yards and three touchdowns, hitting Danny Amendola 11 times for 112 yards. He commanded the pocket with remarkable poise and agility. Brady was a statue in a mosh pit at times, a pogo stick in a phone booth at others. The performance was a finger in the eye to anyone who believed the 40-year-old’s skills are eroding.

That group may include members of his own coaching staff. For the past week, the Patriots listened to — or had to forcibly ignore — reports of internal conflict. According to an ESPN story, reliant on anonymous sources, Bill Belichick had traded Brady’s heralded backup, Jimmy Garoppolo, against his will for a pittance to appease owner Robert Kraft, whose fondness for Brady had transcended New England’s transactional ruthlessness. Meanwhile, Belichick and Brady were at odds over the growing influence of Alex Guerrero, Brady’s health guru, whom Belichick had stripped of privileges around Gillette Stadium as a confluence of Patriots chose Guerrero’s methods over the New England training staff’s.

“The team was focused on Tennessee,” Devin McCourty said. “At this time of year, there’s no such thing as distractions. It comes down to what’s our goal since the beginning of the season.”

Those issues still may need to be sorted out, but the notion of the Patriots in decline seemed frivolous as the New England machine rumbled on Saturday. Next Sunday, they will face either the Pittsburgh Steelers in a rematch of last year’s AFC title game or the upstart Jacksonville Jaguars. One more victory and the Patriots will play for their second consecutive Lombardi Trophy, and Brady and Belichick will appear in their eighth Super Bowl together.

They won for big reasons, and they won for small reasons. After falling behind, the Patriots eschewed huddles and quickened their offensive tempo. The breakneck scheme prevented the Titans from substituting and gave the Patriots’ running backs matchups that gouged Tennessee. James White and Dion Lewis combined for 81 yards on eight catches in the first half, with White scoring on both a reception and a run. That was a big reason — it revived the crowd and allowed the Patriots to seize control.

The Patriots, as ever, were willing to calibrate strategy for specific circumstances to intricate detail. As a matter of vaunted practice, Belichick defers when the Patriots win the coin toss, in hopes of setting up a score immediately before and after halftime. When the Patriots won the coin toss Saturday night, they took the ball. Belichick does not submit to many forces, but one of them is the weather: The wind howled at kickoff and promised to pick up, and Belichick wanted the wind at New England’s back in the fourth quarter. That was a small reason — the game had been decided by the fourth quarter, but Belichick could plan with confidence.

New England’s defense appeared vulnerable early, but as Tennessee suffered injuries to its offensive line, most notably right tackle Jack Conklin, the Patriots’ pass rush started thumping Marcus Mariota, sacking him eight times, a franchise playoff record. The Patriots’ defense, in tatters for the season’s first month, actually yielded the fifth-fewest points in the NFL. That was a big reason — New England proved it can utterly shut down an opponent.

Officiating mattered, too. One early Titans drive stalled near midfield when officials flagged Eric Decker on a phantom pass interference call. In the second quarter, the Patriots were about to punt on fourth and five from their own 14 when an official called a false start on New England, only for the crew to huddle and reverse the call, instead penalizing Tennessee for offside and giving the Patriots a first down. Brady would cap a 16-play drive with a touchdown pass to Chris Hogan. That was a small reason — the Patriots didn’t need favorable calls, but luck never hurts any team.

By the final snaps, it had been forgotten that the Titans had once stunned Gillette Stadium into dead silence. A holding penalty on a punt return set them back to the 5-yard line, a hole Mariota dug out of immediately with a 36-year strike to tight end Delanie Walker, whom the Patriots let roam free despite his standing as Tennessee’s top target. Mariota pushed the Titans downfield, scampering for two first downs, settling them at the New England 15.

Before the snap, Mariota motioned Corey Davis, lined up his left, toward the sideline. Davis burst off the line, faked inside and bolted to the corner of the end zone, a step behind Butler. Mariota floated a pass, and as Davis held off Butler with his right hand, he hauled Mariota’s pass with his left, gorgeous proof of what the Titans saw when they chose him with the fifth pick in April. The Titans, expected to play patsy, held a 7-0 lead.

The quiet would not last — Brady responded with a surgical seven-play drive, and another party at Patriot Place had started. When third-string running back Brandon Bolden plunged in from two yards out in the third quarter, the Patriots moved ahead 28-7. House of Pain’s “Jump Around” blared on the public address system, and the stadium shook. The sky above was dark, and the temperature had dropped into the teens, and nobody wearing Patriots colors seemed to notice.