With only 16 seconds left in overtime, the contest was looking as if it would become the first NFL tie in nearly two years.
But after taking over on the Browns' 37-yard line, Sanchez dropped back and connected with Holmes over the middle. The Jets' receiver took off down the left sideline and scored, notching the win for the Jets (7-2), who took their second straight overtime game.
Holmes finished the game with 76 yards on five catches and Shonn Greene contributed 72 yards on 20 carries for New York.
Colt McCoy went 18-of-31 passing for 205 yards and a touchdown for the Browns (3-6), who also got 82 yards and touchdown on 19 carries from Peyton Hillis.