Trailing 2-0 in their final at-bat, the Twins put two men aboard with two outs against Brian Fuentes (2-1) and Willingham followed by belting 1-0 pitch into the Athletics' bullpen for the walk-off game-winner.
Willingham's stunning blow against his former team made a winner of Glen Perkins (1-1), who managed to hold the A's scoreless in the top of the ninth despite issuing three walks.
Cole De Vries, making his second major league start, blanked the A's on two hits over five innings for Minnesota, which clinched the three-game series.
A's starter Jarrod Parker matched De Vries with six shutout frames, during which he yielded four hits and overcame four walks.
Coco Crisp went 2-for-2 with an RBI for Oakland.