The Tigers were four outs away from taking two of three over first-place Minnesota and inching closer in the AL Central race.
But Detroit paid the price with a costly error in the eighth inning, allowing the Twins to tie the game at three runs apiece before taking the series finale 6-3 in 10 innings.
The Tigers took the lead over their division rivals in the third inning, thanks to a Zach McKinstry double and a Kerry Carpenter single.
Starter Michael Lorenzen allowed two runs over five innings, while Brendan White took the loss in his sixth career appearance.
The Tigers kick off a seven-game road trip Monday at Texas.
