The Twins scored three runs with two outs in the eighth inning, taking advantage of poor defense by the Tigers, according to the Associated Press.
The Tigers led 3-1 when Josmil Pinto singled to left field with runners on first and second. One run scored on the hit, and the tying run scored on an error by left fielder Rajai Davis that also allowed Pinto to reach second base, according to the AP.
Eduardo Nunez followed with an RBI single to make it 4-3 and give the Twins the win.
Twins reliever Jared Burton (1-1) got the win and closer Glen Perkins got four outs for his 10th save.
Twins manager Ron Gardenhire was ejected for the first time this season, after arguing a call in the fourth inning, according to MLB.com. It was the 68th time Gardenhire has been thrown out of a game in his career.
Minnesota begins a three-game series against the Boston Red Sox on Tuesday at Target Field.