Rodriguez had hit safely in 18 consecutive games this season before going 0-for-3 with a walk against Scott Kazmir and Shawn Camp.
The Yankees led 3-to-2 in the seventh until Carl Crawford hit his first career grand slam. Crawford had four hits and scored twice in the Devil Rays' second straight win.
Hideki Matsui hit his first homer of the season for the Yankees, who fell into the American League East cellar at 8-and-11.
Juan Salas retired one batter in the seventh to even his mark at 1-and-1. Al Reyes earned his seventh save with a hitless ninth.
Loser Chien-Ming Wang gave up four runs and nine hits over six and a-third in his season debut.