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.
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.
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.