The Twins built a 6-0 lead and held on to win their fourth in a row. Milwaukee has dropped six straight.
Dozier and Mauer hit solo shots in the fourth and Doumit came through with a two-run blast that gave the Twins a 5-0 advantage. Mauer added an RBI single in the fifth before the Brewers began a comeback that fell short.
Milwaukee's rally was ignited by a three-run triple from Logan Schafer in the sixth.
Minnesota's early success gave the win to P.J. Walters (2-0), who went six innings while giving up four runs on 10 hits. Jared Burton worked a perfect ninth for his second save.
Six of the Minnesota runs came against former Twin Kyle Lohse (1-6), who went 4 2/3 innings while taking the loss.