Playing his former team for the first time since signing a lucrative free-agent deal with the Jets during the off-season, Martin failed to score. He rushed for 107 yards on 28 carries as New York pulled off a stunning win, ending New England's four-game winning streak.
The Jets (2-4), were coming off an embarrassing 30-10 loss in St Louis last week. New England blew away the Kansas City Chiefs a week ago, 40- 10, for their fourth victory in succession.
Testaverde came through with key plays at crucial moments to lead the Jets to their first win in Foxboro for six years.
Improving to 3-0 after starting for the Jets, Testaverde completed 22-of-42 passes for 294 yards and three scores - including a pair of one-yard touchdowns to tight-end Kyle Brady after Martin had been stopped short of the goal-line.
The Jets (3-3), trailed 14-10 following a scoreless third quarter but drove to the Patriots line early in the fourth. Martin was stopped on first down. On the next play Testaverde found a wide-open Brady in the end zone for the touchdown which saw them go ahead for the first time.
Testaverde sealed the win with three minutes 29 seconds to play when he lofted a 43-yard scoring strike down the right sideline to Dedric Ward, who flew past second-year cornerback Chris Canty for his second career touchdown and first this season.
Martin, who missed last week's loss with a bruised right thigh, had twice been stopped short of the goal-line on a drive early in the game. But on third-and-goal from one yard out, Testaverde found Brady to open the scoring. Robert Edwards gained 104 yards on 22 carries and became the first player to score a touchdown in his first six games.
Drew Bledsoe was 18-of-30 for 206 yards and a touchdown for the Patriots, who are now equal with Miami at the top of the AFC East.