By Matthew Geagan, CBS Boston

BOSTON (CBS) — What better way to claim the “Greatest of All-Time” title than with the greatest Super Bowl comeback of all time?

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What was a horrible start turned into an unbelievable end for the New England Patriots, as they won Super Bowl LI 34-28 — the first Super Bowl to go to overtime. They erased deficits for 21-0 and 28-3 against the Atlanta Falcons and their high-powered offense, scoring 31 unanswered points to pull off the incredible comeback.

It’s the fifth Super Bowl win for Patriots head coach Bill Belichick and quarterback Tom Brady, who are now undeniably the greatest at their respective positions. Brady completed 43 of his 62 passes for 466 yards and two touchdowns, going 21-of-27 for 246 yards in the fourth quarter and overtime.

Brady is now the first quarterback with five Super Bowl victories. He was named the game’s MVP, the fourth time he has won the honor.

“I’m so proud of our guys, our coaches, the team. That was unbelievable what we accomplished this season,” Brady said after the victory. “Thank you to all our fans, everyone back in Boston. We love you. You’ve been with us all year and we’re breaking this sucker home!”

NFL commissioner Roger Goodell speaks to Tom Brady #12 of the New England Patriots after defeating the Atlanta Falcons during Super Bowl 51 at NRG Stadium on February 5, 2017 in Houston, Texas. The Patriots defeated the Falcons 34-28. (Photo by Patrick Smith/Getty Images)

NFL commissioner Roger Goodell speaks to Patriots quarterback Tom Brady after New England defeated the Atlanta Falcons during Super Bowl 51 at NRG Stadium on February 5, 2017 in Houston, Texas. The Patriots defeated the Falcons 34-28 in overtime. (Photo by Patrick Smith/Getty Images)

“We got great players and they just compete for 60 minutes, or longer,” Belichick said on the stage after the win.

“Two years ago, we won our fourth Super Bowl down in Arizona. I told our fans that was the sweetest one of all. But a lot has transpired over the last two years, and I don’t think that needs any explanation,” Patriots owner Robert Kraft said after being handed the Lombardi Trophy by NFL commissioner Roger Goodell. “I want to see to our fans, our brilliant coaching staff, and our amazing players who were so spectacular, this is unequivocally the sweetest.”

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LISTEN: Call Of White’s Game-Winning Touchdown on 98.5 The Sports Hub:

The Patriots scored 19 fourth quarter points, with James White capping off a 10-play, 91-yard drive with a six-yard touchdown with 57 seconds left. Tom Brady hit Danny Amendola with a short pass on the two-point conversion, and the receiver fought his way across the goal line to knot things up at 28-28.

In overtime, the Patriots won the coin toss and never gave Atlanta a chance. Brady and company marched 75 yards down the field, with White punching it in from two yards out, his third touchdown on the evening.

White was another gigantic star of the game, catching 14 passes for 110 yards and a touchdown while rushing for two more scores.

The Falcons held a 28-3 lead with 4:14 left in the third quarter, and things looked bleak for the Patriots, who sleepwalked through the firs half. But after New England cut it to 28-12 on a Stephen Gostkowski 33-yard field goal, the defense got them the ball back when Don’t’a Hightower hit Matt Ryan, forcing a fumble that Alan Branch recovered at the Atlanta 25.

Four plays later, Brady hit Danny Amendola for a six-yard touchdown, and a two-point conversion on a direct snap to White cut Atlanta’s lead to 28-20 with 5:56 to go.

The defense forced an Atlanta punt and the Patriots had the ball back with 2:38 left in the game. Julian Edelman made an incredible catch on the drive, hauling in a bobbled ball between three Atlanta defenders, and a few plays later the Patriots had things all knotted up on the White touchdown and Amendola conversion.

Credit: Tom Pennington/Getty Images

Credit: Tom Pennington/Getty Images

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The Patriots victory parade through the streets of Boston will be held on Tuesday at 11 a.m., Boston mayor Marty Walsh announce shortly after the win.