The Tigers scored four times in the eighth inning to top the Twins 4-2 in Minnesota.
Nicholas Castellanos and Niko Goodrum had RBI singles to put Detroit in front and James McCann capped the frame with a two-run double.
Victor Alcantara got the win after starter Spencer Turnbull pitched six innings of one-run ball.
Shane Greene nailed it down with his 32nd save. Trevor Hildenberger took the loss in relief of Kohl Stewart, who allowed two hits over six shutout innings.
Jorge Polanco and Jake Cave drove in runs for Minnesota.