New England Patriots wide receiver Julian Edelman makes a circus catch in the fourth quarter. (Patrick Semansky/Associated Press)

For three quarters, the New England Patriots were outplayed, outclassed and outmuscled by the Atlanta Falcons, shown up so badly on pro football’s biggest stage that only the dreamers and delusional could envision their comeback in Super Bowl LI.

The Patriots’ 34-28 overtime victory at NRG Stadium will go down as the greatest performance of Tom Brady’s career. At 39, after getting sacked five times and pummeled from all sides all night, Brady led his offense to 31 unanswered points to claim a record fifth Super Bowl title for the Patriots, for Coach Bill Belichick, his teammates and the team’s fans.

But the fourth-quarter comeback wouldn’t have been possible without Julian Edelman’s fourth-quarter catch that kept the tying drive alive. It came with the Patriots trailing 28-20 with 2:28 remaining in regulation.

It was Brady’s 51st throw of the game, heaved deep over the middle. After being tipped by cornerback Robert Alford, the ball popped in the air and looked certain to fall incomplete. But the 5-foot-10 Edelman lunged toward it, arms outstretched, and got his fingertips under it as three defenders converged on him like a freeway pileup. Edelmen disappeared under the pile of Falcons, somehow able to secure the ball, clutched tight to his body.

The ruling of a completed 23-yard pass was challenged immediately by Atlanta but was upheld after video replays. The play gave the Patriots the ball at the Atlanta 41.

Social media erupted with hosannas, awe and immediate comparisons to the New York Giants’ David Tyree’s “helmet catch” in the last two minutes of Super Bowl XLII. The catch, which Tyree leapt up to secure against his helmet, was key to Giants’ upset of the unbeaten Patriots and widely remembered as among the greatest plays in Super Bowl history.

Brady and Edelman cast a new contender. “One of the greatest catches I’ve ever seen,” Brady said. “I don’t know how in the hell he caught it.”

“He played lights out all game,” running back LeGarrette Blount added of Edelman. “One of the most amazing catches in Super Bowl history.”

Belichick called it a “tremendous play” and said it only confirmed what he has known about and seen in Edelman since he was drafted by the Patriots out of Kent State in the seventh round in 2009.

“Julian has great concentration,” Belichick said. “He’s as good a competitor as anybody I’ve coached. He has played slot, returned kicks, covered kicks, blocks, catches tough passes, runs the ball. He does whatever it takes.”

Even Edelman seemed dazed by the gymnastics involved, sure of what he’d done but less sure how it would be treated by officials.

“I knew I had a good feel on it. I didn’t know if a piece of the ball was touching. I don’t know what the [catch] rule is. No one knows what the rule is,” he said. “I am pretty sure I caught it.”

Once inside Falcons territory, Brady rolled on, hitting Danny Amendola with a 20-yard completion, the versatile back James White for gains of 13 and seven yards.

And from the 1, White ran behind his right guard for the score that capped the 91-yard that pulled New England within 28-26 at the one-minute mark.

With a successful two-point conversion, Brady passing to Amendola, the Patriots tied it to force overtime. They won the coin toss to start overtime.

And less than four minutes later, White bored in for the game-winning touchdown, and the stadium exploded in confetti and disbelief and Brady fell to his knees.

It was an impossible, improbable ending to a game in which for three quarters, the hardest hits, the leaping catches, the bruising runs were all made by Falcons in red jerseys. It was flat-out dominance.

But even after trailing 21-3 at the half, the Patriots never doubted their ability to come back. “Just do your job,” Belichick said he told his players. And they told one another heading back onto the field that they were about to write an incredible ending.

And after falling behind 25 points in the third quarter, Brady kept slinging it, and his teammates knew he would bring them back. An assassin, they called him. A quarterback who would tear your heart out.

But Brady was close to tears when he finally found his parents, who had made the trip despite his mother’s illness, and his own family.

And the legions of Patriots fans who had traveled to Houston to celebrate a fifth Super Bowl championship got their chance to boo NFL Commissioner Roger Goodell, as he presented the Vince Lombardi Trophy.

It was the ending they wanted to see after the league’s near two-year Deflategate controversy, which ended with Goodell suspending Brady for the first four games of the regular season.

The boos subsided as Patriots owner Robert Kraft held the trophy aloft and reminded them that two years earlier in Phoenix, which the Patriots had won their fourth Super Bowl on a heart-stopping interception, he felt it was the sweetest victory of all.

“But a lot has transpired during the last two years,” Kraft said, alluding to the controversy that also cost him a $1 million fine and the team, two draft picks. “I want to say to our fans, our brilliant coaching staff, our amazing players: This is unequivocally the sweetest.”