Rodriguez led off the eighth inning with his 30th home run of the year. It was the 548th career homer for the reigning American League MVP, tying former Philadelphia Phillies Hall of Fame third baseman Mike Schmidt for 12th on the all-time big league list.
Mike Mussina (17-7) allowed two runs on 10 hits while walking one and striking out eight for the Yankees.
Damaso Marte along with Joba Chamberlain and Dan Giese, who were both activated off the disabled list before the game, combined for three innings of scoreless relief.
Cliff Floyd and Shawn Riggans each had an RBI for Tampa Bay, which lost for the first time in six games but still leads the AL East by four games over the Red Sox. Matt Garza (11-8) surrendered six runs on five hits in five-plus innings.