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After both teams were forced to punt off their opening possessions, the Jets got the first points on the board when Bilal Powell was tackled short looking for a rushing touchdown, leaving Randy Bullock to kick the field goal.
Dwayne Harris handed the Giants the lead at the start of the second quarter though as the Jets were forced to punt following a sack on Ryan Fitzpatrick, leaving the punt returner to sprint back 80 yards to the endzone.
Powell briefly got the designated visitors back on level terms when he collected a shuttle pass from Fitzpatrick, weaving through a couple of defensive players to cross the line.
Eli Manning needed just over a minute to put the home side back in front though, launching a deep pass to Odell Beckham Jr, who beat two defenders for pace down the sideline to pick up a 72-yard touchdown, while Josh Brown added another field goal before the break, leaving the Giants 10 points up at half time.
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Both teams put together lengthy drives in the third quarter, but the Giants were forced to punt after a nine-play possession stalled, while the Jets also failed to add to their score after a drive that lasted for more than five minutes.
The Giants strung together another long drive as Manning on the offense came back onto the field, but the quarterback threw an interception after more than 11 minutes on the field while looking to Rueben Randle for the touchdown.
Ivory and Eric Decker both had receptions as the Jets tried to make the most of the turnover, but the AFC East side had to send on their kicker after Pierre-Paul prevented Decker from getting into the endzone, leaving Bullock to split the uprights.
The Jets still needed a touchdown and extra point to level the scores inside the final four minutes, but quickly forced a punt from the Giants before Fitzpatrick looked to Brandon Marshall on the left, leaving the wide receiver to stretch for the catch in the corner of the endzone.
The Jets got the ball first in overtime, but Decker and Powell both missed chances to score the game-winning touchdown, leaving Bullock to kick another field goal, while giving the Giants a chance to snatch victory.
Beckham got the hosts into field goal range, but Brown, who had not missed so far this season, saw his 48-yard attempt drift wide of the left post, handing the Jets the win.
The result gives the Jets back-to-back wins in the NFL, keeping them in the playoff hunt, while the Giants slip to 5-7.