Sanchez found LaDainian Tomlinson and Braylon Edwards with second-period scoring strikes, putting New York ahead for good. The Jets hung on to avenge last month's 45-3 loss to the Patriots by eliminating the AFC's top seed from the post-season.
The Jets advanced to play the Pittsburgh Steelers next week for the right to represent the AFC in the Super Bowl.
Sanchez also connected with Santonio Holmes on a 7-yard TD pass early in the fourth quarter to put the Jets up 21-11. He went 16-of-25 through the air for 194 yards and no interceptions.
Jerricho Cotchery made five grabs for 96 yards and Shonn Greene carried the ball 17 times for 76 yards and a score for New York.
Tom Brady completed 29-of-45 passes for 299 yards and two scores for New England, which had an eight-game winning streak snapped. He was intercepted once.