HOUSTON — Tom Brady led one of the greatest comebacks in sports history highlighted by an unbelievable Julian Edelman catch that helped lift New England from a 25-point hole against the Atlanta Falcons to the Patriots’ fifth Super Bowl victory, the first ever in overtime.

The Patriots scored 19 points in the final quarter, including a pair of 2-point conversions, then marched relentlessly to James White’s 2-yard touchdown run in overtime to beat the Atlanta Falcons 34-28 Sunday night.

Brady, the first quarterback with five Super Bowl rings, guided the Patriots (17-2) through a tiring Atlanta defense for fourth-quarter touchdowns on a 6-yard pass to Danny Amendola and a 1-yard run by White, which came with 57 seconds remaining in regulation. White ran for the first 2-pointer and Amendola did the deed with a reception on the second.

Brady, winning Super Bowl MVP for a record fourth-time, finished 43 for 62, the most attempts in Super Bowl history, for 466 yards, also a record, and two touchdowns.

“You know, we all brought each other back,” Brady said. “We never felt out of it. It was a tough battle. They have a great team. I give them a lot of credit. We just made a few more plays than them.”

Before the stunning rally — New England already held the biggest comeback in the final period when it turned around a 10-point deficit to beat Seattle two years ago — the Falcons (13-6) appeared poised to take their first NFL championship in 51 seasons. Having never been in such a pressurized environment, their previously staunch pass rush disappeared, they stumbled on offense and Brady tore them apart.

“Deflategate” far behind them, Brady and coach Bill Belichick won their 25th postseason game, by far a record. The Falcons added to Atlanta’s long history of pro sports frustration.

Belichick became the first coach with five Super Bowl crowns.

The Patriots won the coin toss for overtime and it was no contest. Brady completed six passes against an overmatched Falcons secondary. A pass interference call took the ball to the 2, and White scooted to his right and barely over the goal line.

His teammates streamed off the sideline to engulf White as confetti streamed down from the NRG Stadium rafters.

It was almost an impossible dream for the Patriots a bit earlier. But helped by Matt Ryan’s fumble on a sack, a Edelman’s catch off of a defender’s shoe, and Brady’s passing, they never stopped coming.

White scored three touchdowns and had 14 receptions for 110 yards, but Brady hit seven different receivers.

Until the Patriots took charge with their late surge, league MVP Ryan was outplaying Brady. It didn’t last.

Atlanta’s string of touchdowns on its opening drive ended at eight, though Devonta Freeman sprinted for 37 yards on the Falcons’ first offensive play. The drive was stunted when Ryan was sacked by Trey Flowers, New England’s leader in that category.

Then it was Atlanta’s D that went sacks-happy, getting two on the Patriots’ next drive in what would be a scoreless opening quarter. Who expected that? Well, New England has not scored a point in the first 15 minutes in Brady’s seven Super Bowls.

It sure looked as if the Patriots would get on the board immediately in the second period as Brady and Edelman connected twice for 40 yards. But Blount’s fumble turned the momentum to the Falcons, who then took their biggest lead in a Super Bowl — yeah, we know, they have been here only twice — on Freeman’s 5-yard run to cap a quick 71-yard drive on which Jones came alive.

Jones showed why he is an All-Pro receiver with a tough leaping catch over the middle for 19 yards, then got open on the sideline for 23. Freeman did the rest.

Before New England could catch its breath, Ryan had the Falcons up by 14. Using the no-huddle attack to perfection, he threw for 51 yards on a 52-yard drive, hitting Hooper with a pinpoint pass in the left side of the end zone.

Then Brady was victimized by his own poor decision, a rarity on the big stage. Atlanta was called for defensive holding three times on third downs to keep the drive alive. From the Falcons 23, under pressure Brady tried to squeeze a throw to Danny Amendola. Alford stepped in and sprinted, then glided 82 yards for the second-longest pick-6 in a Super Bowl — and Brady’s first.

Shockingly, it was 21-0.

New England gathered its wits for a 52-yard drive to Stephen Gostkowski’s 41-yard field goal. Still, it was 21-3 when Lady Gaga took the stage.

There was smoke hanging over the field when both teams had three-and-outs to open the third quarter. It was a mirage regarding Ryan and Co., who marched 85 yards to Coleman’s 6-yard TD catch on a swing pass. While New England scored the next nine points on James White’s 5-yard TD reception — the extra point was missed by Gostkowski, who later made a 33-yard field goal.