Jason Kipnis clubbed a go-ahead, three-run homer in the sixth inning as the Indians topped the Twins 5-3 in Cleveland.
Yonder Alonso singled in the tying run in the sixth before scoring on Kipnis' blast as the Tribe took the rubber match of the three-game set.
Mike Clevinger pitched into the seventh inning for the win and Brad Hand notched his sixth save.
The Indians open up a three-game series with the Rays tonight at Progressive Field.
Corey Kluber will take the ball for the Tribe, which holds a 14-game lead on Minnesota atop the AL Central.
Tampa Bay will counter with Tyler Glasnow.