With the game tied 4-4 in top of the 10th, Jake McGee (0-1) relieved Kyle Farnsworth to start the frame and Willingham greeted him by launching a 3-2 fastball over the left-field fence.
Hideki Matsui added a two-run homer as the A's took the rubber match of a three-game set at Tropicana Field.
Fautino De Los Santos (1-0) collected his first major league victory after tossing a scoreless bottom of the ninth and Andrew Bailey registered his 13th save despite allowing a pair of hits in the bottom of the 10th.
The Rays were led at the plate by Evan Longoria and Casey Kotchman, each of whom hit solo homers, and by Desmond Jennings' three hits.
Tampa Bay starter David Price lasted just 4 2/3 innings after surrendering four runs on seven hits.
Celebrity Families of 2014 [PHOTOS]