Conor Jackson, Hideki Matsui and Cliff Pennington also knocked in a run apiece for Oakland, which earned a split in the series and has won three of its last five overall. Mark Ellis had a pair of doubles and scored a run in the victory.
"Great job by Trevor today," Oakland manager Bob Geren said. "He definitely answered the challenge, going eight innings and throwing 112 pitches."
Casper Wells accounted for the only offense with a homer for the Tigers, who have dropped two in a row after winning the previous four.
Brad Penny (0-2) suffered the loss after yielding five runs on four hits, with four walks in five-plus innings of work. The veteran right-hander struck out five.
Oakland manufactured a run in the fourth to open the scoring. Daric Barton drew a leadoff walk and went to third on a single by Jackson. After Willingham struck out, Matsui's groundout plated Barton.
The Athletics then tacked on three more in the fifth. Landon Powell led off with a double and the next two batters were retired before David DeJesus was hit by a pitch and Barton walked. A free pass to Jackson forced in a run and Willingham followed with a two-run single through the left side for a 4-0 game.
Wells' homer leading off the sixth got the Tigers on the board, but Oakland got the run back in the home half on Pennington's sacrifice fly.
Cahill stranded a runner in the seventh, worked around a leadoff single in the eighth and was lifted after throwing 112 pitches -- 80 for strikes -- in favor of Tyson Ross in the ninth.
The young right-hander gave up a leadoff single to Austin Jackson before settling down to strikeout Brennan Boesch and Miguel Cabrera. Ryan Raburn then flied out to left to end the game.