Cuddyer hit an RBI groundout in the bottom of the fourth inning and an RBI single in the sixth. One of Monroe's two hits was a two-run homer in the eighth.
Joe Nathan earned his 10th save.
Detroit's run scored on Curtis Granderson's solo homer in the top of the eighth. He had two of the Tigers' six hits.
Losing pitcher Justin Verlander (1-5) gave up four earned runs and seven hits in seven innings with two walks and five strikeouts.