Coco Crisp capped a four-run ninth inning with 5, hampering Los Angeles' hopes to reach the playoffs.
The Angels are three games behind Boston with three remaining. The Red Sox lost to the Yankees in the opener of a doubleheader Sunday, but won in 14 innings in the night contest in the Bronx. The Angels, who host AL West- champion Texas to conclude the season, are also two games behind Tampa Bay.
Josh Willingham led off the ninth with a homer to left-center field. Scott Sizemore and Chris Carter hit one-out singles. Adam Rosales followed with a grounder back to pitcher Jordan Walden (5-4), who threw wildly to second. A run scored on the play and runners were set up on the corners. Kurt Suzuki kept the rally going with an RBI double down the right-field line. Jemile Weeks was intentionally walked to load the bases. Hisanori Takahashi then gave up Crisp's sac fly to make it 6-5 A's.
Andrew Bailey worked around a two-out walk in the ninth to secure Oakland's third win in four games.
"We came back against a team fighting for a playoff spot," A's manager Bob Melvin said. "Probably the best win I've seen for us this season."
A's starter Rich Harden gave up three runs on eight hits over six innings. Fautino De Los Santos (3-2) got the win despite giving up two runs in the eighth.
LA starter Joel Pineiro pitched 6 1/3 scoreless frames, giving up three hits and striking out four.
The Angels took the lead in the first inning. Howie Kendrick hit a one-out triple to center and scored on Bobby Abreu's base hit.
Abreu added a solo homer to right in the third for a 2-0 lead. Vernon Wells hit a solo shot to left-center in the sixth to give Los Angeles a three-run edge.
The A's loaded the bases with one out in the eighth. Weeks hit an RBI single and Crisp added a sac fly to cut the gap to 3-2.
Peter Bourjos got both runs back in the home half on with a two-run bloop double to right.
"It hurts to lose a game like that," Angels outfielder Torii Hunter said.
Oakland went 11-8 against the Angels this season...The A's were without shortstop Cliff Pennington (left oblique).