Baker, making his first start since July 5 due to elbow soreness, didn't miss a beat in his return, holding Detroit to three hits while walking one and striking out five.
Anthony Swarzak gave up a run after Baker left the game but Phil Dumatrait and Glen Perkins each tossed a scoreless inning in relief and Joe Nathan racked up his seventh save as Minnesota broke an 11-game losing streak to the Tigers.
Danny Valencia clouted a solo homer in the second inning and Delmon Young added a two-run double in Minnesota's victory.
Tigers starter Brad Penny (7-7) yielded four runs on seven hits in a seven-inning effort.
Miguel Cabrera drove in the only run for Detroit, which entered the game with a 1 1/2-game lead in the American League Central.