Gostkowski also nailed a 43-yarder with 5 seconds left in regulation to force overtime for the Patriots (4-3), who had blown a 10-point lead in the fourth quarter and found themselves trailing 26-23.
New England sealed the win when Rob Ninkovich and J. Cunningham sacked Jets quarterback Mark Sanchez on New York's overtime possession, forcing a fumble that Ninkovich recovered to end the game.
Tom Brady connected on 26-of-42 pass attempts for 259 yards and two touchdowns -- both of which went to Rob Gronkowski (six catches, 78 yards).
Sanchez (28-of-41, 328 yards, one TD, one interception) found Dustin Keller on a 7-yard scoring pass and helped set up a pair of Nick Folk field goals during the Jets' late-game rally.
Jeremy Kerley made seven catches for 120 yards for New York (3-4).
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes