The Falcons have been in existence for 51 years and Sunday was just their second Super Bowl appearance in team history. For 59 minutes, they were leading, and for 45 minutes, they were dominating a Patriots team that seemed helpless to do anything about it.

But the Patriots overcame a 25-point deficit to take the game to overtime. They then won it, 34-28, on the very first series after James White dived in from two yards out. The 31 unanswered points in the thrilling comeback cements the Patriots' legacy as the greatest NFL franchise this century.

It was New England's ninth Super Bowl appearance in team history, and the seventh in the Bill Belichick-Tom Brady era. And if not for Eli Manning and the Giants, Bill and Tom would be 7-0 in the championship game. We're guessing they'll settle for 5-2, especially given the "THAT DID NOT JUST HAPPEN" way they went about winning this one.

We won't lie: We were convinced this game was over at halftime; the Falcons led 21-0 late in the second quarter, 28-9 to start the final quarter, and 28-20 at the two-minute warning. You might notice that with each update the Patriots crept closer while the Falcons went from confident to hopeful to apprehensive to dejected as Brady marched New England down the field again and again and again and again, until the they had even out-Patriots'd the Patriots.

Not only did the Pats overcome the largest deficit in Super Bowl history, they played in the first overtime game in Super Bowl history, and oh, by the way, Brady set a Super Bowl record for passing yards. (And before you say, yeah, but he had the benefit of overtime, we'll kindly point out that he managed the feat before the end of regulation.)

And regarding those insurmountable comebacks, Brady now has four of them:

How 'bout that Patriots defense?

But for as amazing a performance as Brady put on in the second half and that first drive of overtime, we have to acknowledge what the Patriots' defense was able to do over that same span. We wrote about it in the days leading up to the Super Bowl: Defensive coordinator Matt Patricia faced the near-impossible task of slowing a Falcons offense that obliterated the Seahawks and Packers in the playoffs, and at one point, it seemed clear they were going to do the same to the New England. At one point in the first half, Atlanta had outscored those three teams 108-44 over the last month.

And it's that kind of offensive firepower, which appeared able to score at will, that will earn Falcons offensive coordinator Kyle Shanahan the 49ers' head job and did earn Matt Ryan well-deserved MVP honors. It's not an exaggeration to say that this was as close to unstoppable a unit as we've seen since, incidentally, the 2007 Patriots, which regularly blew out every opponent they faced right up until the moment they ran into aforementioned Giants in the Super Bowl.

For the first 30 minutes, the Patriots were incapable of stopping the Falcons' running game, even though New England entered the game as one of the league's best run defenses (they ranked fourth, according to Football Outsiders). In fact, after Devonta Freeman scored the Falcons' third series, which led to the first points of the game early in the second quarter, Atlanta had 85 rushing yards and Ryan had just four completions.

Yes, the Patriots had shut down Julio Jones (for the time being), but it came at a cost. Freeman's niftiness, coupled with running plays designed to attack the perimeter and stretch New England's defense, opened up running lanes that were easily exploited.

Following a Patriots three-and-out, Ryan and the passing game finally got to work. He hit Taylor Gabriel for 24 yards, and then found Jones for 18 more (and, yeah, he was double-covered and still caught it). Then on third down, Ryan found tight end Austin Hooper in the end zone and the Pats were on the ropes.

Things got worse before they'd get better ...

Another Tom Brady first -- a Super Bowl pick-six

Trailing 14-0 and desperately trying to put a dent in the Falcons' lead, Brady, who had been uncharacteristically pressured early in the game, marched the Patriots down the field, thanks in part to three Falcons defensive holding calls -- all on third down, all keeping the Pats on the field. And then Brady, again uncomfortable in the face of a pass rush, forced a throw that was intercepted by Robert Alford and taken to the house.

This is no coming back from that, right? RIGHT?!

Wrong, it turns out.

One half of football is not like the other

We often hear about Belichick's prowess when it comes to in-game adjustments, and he and Patricia again proved themselves on Sunday. Because shortly after Lady Gaga fell from the roof -- seriously, we have to mention this because we are all guilty of jumping to conclusions -- the Pats' defense was a completely different unit.

OK, back on Earth ...

The Falcons went three-and-out on their first drive, and Tevin Coleman scored on a six-yard touchdown reception a drive later to extend the score to 28-3. But with 6:25 left in the third quarter, Atlanta had scored its last points.

New England, meanwhile, embarked on their run of 31 unanswered, and early in the fourth quarter with the Falcons leading 28-12, the Pats' defense finally got to Ryan. Freeman whiffed on a block, and Dont'a Hightower made everybody pay:

The Patriots scored five plays later, and then converted the two-point conversion to cut it to eight.

Commence 'bend but don't break' defense

By this point, no one would've blamed the Falcons for puckering up. It was now a one-score game against the best coach and quarterback in league history. But credit to Shanahan and Ryan for not turtling up. Instead of running the ball to try to take time off the clock (there was still some six minutes left), they instead threw on first down. Good things happen when you take chances.

But that was the opening act, because Julio Jones, who had shown glimpses of his Julio-ness at points in the evening, just decided to take the game over. Here's what happened two plays after Freeman's reception above:

That is the best 27-yard reception in the history of football -- pick-up, flag, high school, college or professional.

My Lord.

Think about just how amazing that was. Jones was double-teamed, and Eric Rowe, who is 6-foot-1, was fronting him and missed getting his hands on the ball by millimeters. But Jones maintained his focus and not only caught the pass, he inexplicably got both feet down.

It wasn't a touchdown, though, which meant the Patriots would live to fight another play. So after Freeman was tackled for a one-yard loss, and the Falcons faced second-and-11 from the New England 23-yard line, Ryan dropped back to pass. The one thing he couldn't do was take a sack.

He took a sack.

It got worse. On third-and-23, Jake Matthews was called for holding, and on third-and-33, Ryan was pressured, and threw incomplete. Falcons had to punt.

Patriots were very, very good, but also pretty lucky

Despite the Falcons' slow-motion implosion, they still had opportunities to win. Twice on the Patriots' final drive of regulation, Atlanta defenders were close to making interceptions. The first fell incomplete. The second ended up as a 23-yard "WHAT? WHAT?!" completion to Julian Edelman.

Behold:

Four plays later, the Patriots scored another touchdown -- and then converted another two-pointer. The score was tied with 57 seconds remaining in regulation and the Falcons' sideline looked like they were on the business end of a zombie apocalypse.

By the time the Patriots won the overtime coin toss, the game already felt over. Brady needed just eight plays to get New England in the end zone one last time:

Ryan and that offense never saw the field in overtime.

Deflategate is a scandal best served cold

Hey, Roger Goodell, looks like the invitation to return to Gillette Stadium remains open.

Maybe the only person more excited than Patriots owner Bob Kraft is Brady's wife:

Finally, it's worth noting that the Pats did all this without one of their best players.

Put another way: Expect New England to open as favorites to win the Super Bowl next season too. But we're guessing you already knew that.

Relive all the magic of the Super Bowl LI live blog below.