Inge, who was released by Detroit in late April, lined a pitch from Blue Jays closer Francisco Cordero (1-2) over the left field wall to cap a five-run ninth inning that rallied the A's to their fifth win in their last seven games.
Cordero had come into the bottom of the ninth with a 3-2 lead after Kelly Johnson singled in a tie-breaking run in the top of the inning. Cordero allowed a leadoff double to Michael Taylor, who scored on a single by Cliff Pennington to make it 3-3.
Grant Balfour (1-1) was the windfall winner thanks to Inge's heroics. Josh Reddick had two RBI for the A's.
Johnson had three hits and two RBI to lead the Jays.