Baker (8-5) returned from the disabled list and worked five scoreless innings, allowing just three hits while striking out five, to lead the Twins to a 4-1 victory and break an 11-game losing streak to the Tigers.
Joe Nathan worked around a Jhonny Peralta double to record his seventh save of the season.
Delmon Young belted a two-run double and Danny Valencia hit a solo homer for the Twins.
Brad Penny (7-7) allowed four runs on seven hits and three walks over seven innings.
Miguel Cabrera knocked in the only run for the Tigers, who won the first two contests of this four-game series and hadn’t lost to the Twins since September 1, 2010.
Ben Revere set the table in the first with a walk, advanced to second on Joe Mauer’s groundout and scored on Michael Cuddyer’s single to left.
Valencia doubled the margin with a leadoff shot in the second.
Jason Kubel, who was reinstated from the disabled list on Friday, began the fourth with a single and Valencia followed with a walk, before Young doubled to center, giving the Twins a 4-0 lead.
Baker, who had been on the DL since July 7 with a right flexor strain, allowed runners to reach the corners with two down in the opening frame but escaped the jam and cruised through five masterful innings.
It wasn’t until he left in favor of Anthony Swarzak that the Tigers finally broke through, as Cabrera’s 24th double of the season plated Brennan Boesch, who reached with a one-out single and advanced to second on Magglio Ordonez’s groundout.
The Tigers were 1-for-8 with runners in scoring position…Baker has not allowed a home run in his last six starts…The Tigers’ 11-game win streak over the Twins was the longest-ever string of victories over the club.