Donaldson had two runs and one RBI, adding to scores from Jed Lowrie and Eric Sogard to give the A's their ninth consecutive win.
Brayan Villarreal (0-2) stepped onto the mound in the bottom of the 12th inning and struck out Chris Young before giving up the homer and the game at Oakland-Alameda County Coliseum.
Prince Fielder contributed a three-run homer in the Tigers' loss.
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