GLENDALE, Ariz. (AP) — The Giants had the perfect answer for the suddenly imperfect Patriots: a big, bad defense and an improbable comeback led by their own Mr. Cool quarterback, Eli Manning.

In one of the biggest upsets in Super Bowl history, New York shattered New England’s unbeaten season 17-14 Sunday night as Manning hit Plaxico Burress on a 13-yard fade with 35 seconds left. It was the Giants’ 11th straight victory on the road and the first time the Patriots tasted defeat in more than a year.

It was the most bitter of losses, too, because 12-point favorite New England (18-1) was one play from winning and getting the ultimate revenge for being penalized for illegally taping opponents’ defensive signals in the season-opener against the New York Jets.

But its defense couldn’t stop a final, frantic 12-play, 83-yard drive that featured a spectacular leaping catch by David Tyree, who had scored New York’s first touchdown on the opening drive of the fourth quarter.

‘‘It’s the greatest feeling in professional sports,’’ Burress said before bursting into tears.

‘‘That’s a position you want to be in,’’ said Manning, who followed older brother Peyton’s MVP performance last year with one of his own. ‘‘You can’t write a better script. There were so many big plays on that drive.’’

And now the 1972 Miami Dolphins can pop another bottle of champagne in celebration of a record still intact, the only perfect season in the Super Bowl era.

The Patriots were done in not so much by the pressure of the first unbeaten season in 35 years as by the pressure of a smothering Giants pass rush. Tom Brady, the league’s Most Valuable Player and winner of his first three Super Bowl, was sacked five times, hurried a dozen more and at one point wound up on his knees, his hands on his hips following one of many poor throws in New England’s lowest scoring game of the season.

‘‘They played well,’’ Patriots coach Bill Belichick said. ‘‘They made some plays. We made some plays. They just made a few more. We played as hard as we could. We just couldn’t make enough plays.’’

Hardly a familiar position for the record-setting Patriots and their megastar quarterback. And a totally strange outcome for a team that seemed destined for historic glory.

Oddly, it was a loss to the Patriots that sparked New York’s stunning run to its third Super Bowl and sixth NFL title. New England won 38-35 in Week 17 as the Patriots became the first team in 35 years to go spotless through the regular season. But by playing hard in a meaningless game for them, the Giants (14-6) gained something of a swagger and Manning cast found his footing.

Their growing confidence carried them through playoff victories at Tampa, Dallas and Green Bay, and then past the mightiest opponent of all.

Not that the Patriots were very mighty this day. They even conceded with 1 second on the clock as coach Bill Belichick ran across the field to shake the hand of jubilant Giants coach Tom Coughlin, then headed to the locker room, ignoring the final kneeldown.

That it was Manning taking that knee was stunning. He not only matched his brother’s achievement of last year with the Indianapolis Colts, but he showed the brilliant precision late in the game usually associated with, well, Brady.

Peyton Manning was seen in a luxury box jumping up and pumping both fists when Burress, who didn’t practice all week because of injuries, caught the winning score.

‘‘We just hung in there on offense, kept executing,’’ said Burress, who wasn’t far off on the 23-17 prediction he made a few days ago. ‘‘It came down to one play and we made it.’’

The Giants became the first NFC wild card team to win a Super Bowl; four AFC teams have done it. They also are the second wild-card champions in three years, following the Pittsburgh Steelers after the 2005 season.

The upset also could be viewed as a source of revenge not only for the Giants, but for the other NFL teams over Spygate back in September. That cheating scandal made headlines again late in Super Bowl week, and could have placed an infinite cloud over New England’s perfection.

Until the frantic fourth quarter, the only scoring came on the game’s first two drives.

The Giants did almost exactly what they sought with the opening kickoff, using up nearly 10 minutes to go 63 yards. Almost exactly, but not quite, because they settled for a 32-yard field goal after converting four third downs on the 16-play series. The 9:59 drive was the longest in Super Bowl history.

That 3-0 lead lasted for the rest of the quarter, but only because the Patriots were stopped at New York’s 1 as the period expired. On the next play, Laurence Maroney scored.

New England’s 12-play drive was aided by a 16-yard pass interference penalty on linebacker Antonio Pierce in the end zone. It began with Maroney’s 43-yard kickoff runback.

It was the fewest possessions in the first quarter of a Super Bowl.

New York’s first series of the second quarter looked dangerous after Amani Toomer’s lunging sideline catch for 38 yards. But rookie Steve Smith mishandled Manning’s throw at the New England 10, Ellis Hobbs intercepted and returned it 23 yards.

Those are opportunities teams can’t waste against a strong opponent, let alone the Patriots. It was Manning’s first interception of the postseason, albeit entirely not his fault; the last was by Hobbs in the season finale.

The Giants survived rookie Ahmad Bradshaw’s fumble, which he recovered, on their next series, because their league-leading pass rush came alive when the Patriots got the ball back. New York sacked Brady on successive plays, forcing a punt, but the Giants’ were hurt by an illegal batting of the ball penalty on Bradshaw after reaching the New England 25.

Justin Tuck’s second sack, in the final seconds of the half, forced a fumble recovered by New York teammate Osi Umenyiora. The Giants’ celebrated defensive line controlled much of the half, holding the most prolific offense in NFL history to a measly 81 yards and seven points. New England had the ball only 10:33.

But New York’s mistakes left it with just three — and there are no moral victories in Super Bowls.

So the Giants got a real one as the maturing Manning hung in to find Tyree for a 5-yard touchdown to cap an 80-yard drive for a 10-7 lead.

Pressed unlike they are accustomed to, the Patriots responded with their own 80-yard march as Brady finally got some time. Randy Moss, who caught a record 23 of Brady’s record 50 TD throws this year, took a 6-yard pass when cornerback Corey Webster fell, and with a mere 2:42 remaining, the first 19-0 season was right there.

Eli and the Giants snatched it away.