The Athletics trailed 5-0 after two innings but chipped away at the lead. Eric Sogard (3-for-4, two RBI) got Oakland on the board in the third with an RBI single and Cespedes added a two-run double, cutting the deficit to 5-3.
After a Brandon Moss fielder's choice grounder produced another run in the fifth, Cespedes drove him in with a single for the tying run.
The Angels went back in front 6-5 in the sixth on an RBI double from Erick Aybar, but Oakland then exploded for five runs in the bottom of the frame, sending 10 men to the plate.
Stephen Vogt, Sogard, Jed Lowrie and Moss each provided an RBI before Cespedes completed his day with a run-scoring two-bagger, handing the A's a third straight win over the Angels.
Jesse Chavez (2-2) notched the win with two scoreless relief frames as the American League West-leading Athletics upped their lead over second-place Texas to six games.
Los Angeles reliever J.C. Gutierrez (0-2) absorbed the loss.