New York trailed 6-4 heading into the bottom of the sixth, but managed a run in that inning on a sacrifice fly, scored an unearned run in the eighth to tie it and produced the game-winner without the benefit of a hit in the ninth.
Jeter reached in the ninth on a one-out walk from Brayan Villarreal (0-1), moved to second on a walk to Curtis Granderson and went to third on a wild pitch. He scored from there when a 3-0 pitch to Alex Rodriguez from Villareal got away from catcher Alex Avila.
The pitch was in the dirt and bounced away from Avila after hitting a shin pad.
The ninth-inning run made a winner out of Mariano Rivera (1-1), who retired the side in the top half of the frame.
Rodriguez hit a solo homer for the Yankees in the fourth and Russell Martin had a two-run shot in the fifth.
Detroit starter Justin Verlander gave up four runs on seven hits in six innings without figuring in the decision.
Boston schools pull out free condoms over wrapping complaints
Aaron Carter is still in love with Hilary Duff