Nick Green added a solo shot for Tampa Bay, which ended a four-game slide.
Winner Scott Kazmir (1-4) yielded two runs on three hits in 5 2/3 innings. He had four walks and two strikeouts before leaving the contest after getting hit on the left thigh by a liner by Rondell White in the sixth.
Danys Baez worked 1 1/3 scoreless innings to record his fourth save of the season.
Loser Mike Maroth, a last-minute starter, dropped to 4-3.
White and Dmitri Young both had RBI singles for the Tigers.