The Tigers had a three-game winning streak snapped despite a solid seven-inning effort by starting pitcher Armando Galarraga.
Detroit rallied from a 3-1 deficit to tie it in the sixth on Miguel Cabrera's two-run homer but the Tigers could not manage another run.
Galarraga allowed only four hits before being replaced by Phil Coke (7-5) in the eighth and Coke loaded the bases on two singles and an intentional walk. Wieters than lifted a fly ball to right that brought home pinch-runner Julio Lugo with the go-ahead run and Adam Jones delivered an RBI single later in the inning.
Another sacrifice fly in the ninth by Brian Roberts finished the scoring.
David Hernandez (6-8) picked up the win with one inning of relief. Koji Uehara was perfect in the ninth while earning his eighth save.