Correira (5-4) snapped a two-start losing streak, holding the Brewers to three runs on seven hits over six full frames. The right-hander walked one and struck out four.
Josh Roenicke, Brian Duensing and Jared Burton combined for two innings of scoreless relief and Glen Perkins hurled a 1-2-3 ninth for his 10th save as the Twins took the opener of a four-game interleague rivalry series.
The Twins were clinging to a 2-1 lead in the fifth when they loaded the bases with two outs against Brewers starter Wily Peralta and Doumit came through with a grounder up the middle for two RBI.
Joe Mauer homered and scored three runs while Chris Parmelee also went deep in the victory.
Peralta (3-6) allowed four runs (three earned) on five walks and five hits over five full frames.
Carlos Gomez bashed a pair of solo homers for the Brewers.