Detroit won for the second time in eight games since sweeping the Yankees in a three-game series in New York. It was the Tigers' first sweep of at least three games at Yankee Stadium since 1966.
Kei Igawa's season debut was a forgettable one for New York. He lasted just three-plus innings, allowing six runs on 11 hits.
In the third inning, Rodriguez drove in a run with an infield double, and Magglio Ordonez and Gary Sheffield also had run-scoring hits to give Detroit a 4-1 lead.
The Tigers scored two more in the fourth, on left-fielder Hideki Matsui's error and Placido Polanco's RBI single.
Jason Giambi homered in the second off Rogers, giving him 184 with the Yankees, passing Tommy Henrich and tying Charlie Keller for 16th place in team history.
New York added three runs off reliever Todd Jones in the ninth, on Cano's RBI groundout, Jeter's run scoring single and Bobby Abreu's RBI double before Shelley Duncan lined out to center to end the game.
