Pinch-hitter Gary Matthews Jr.'s two-out RBI single had given the Angels a one-run lead in the seventh, 10-9, but Kurt Suzuki drove in the tying run with a two-out single in the eighth and Jack Cust followed with an RBI double.
Matt Palmer took over for Kevin Jepsen, and Daric Barton delivered an RBI single with his career-best fourth hit. Mark Ellis' three-run homer sent fans to the exits.
"They had, what, 19 hits?" Angels manager Mike Scioscia said, studying the stat sheet. "It's hard to say one hit is the difference."
But he cited Suzuki's hit as "obviously a key point in the game. If we get that out, we can turn it over to Brian [Fuentes] to finish.
"Those guys [batting with runners] in scoring position were terrific, and with two outs and runners in scoring position, they were terrific. We just couldn't hold them."
The A's were 8-for-17 with runners in scoring position, while the Angels -- leading the Majors in that department at .295 -- were 4-for-14.
Angels ace John Lackey, presented a 9-2 lead when his team scored six times in the fourth, yielded four runs in the fifth and departed having surrendered six earned runs on 10 hits.
"After the first inning he started to make better pitches," Scioscia said of Lackey, who endured a 34-pitch opening inning in falling behind 2-0. "He had trouble in the fifth. He says he feels fine."
The bullpen was unable to shut down sizzling Oakland, which won for the 16th time in 20 games and 11th in the past 13.
The Angels became the final team in the Majors to lose four consecutive games. Not since the 2005 Cardinals had a team gone all season without a four-game slide.
The fourth A's pitcher, Craig Breslow, moved to 8-7 with the win as Jepsen (6-4) absorbed the loss.
Suzuki and Cust each drove in four runs with three hits, and Ellis drove in those three with just one hit.
"We could've rolled over and let the Angels have the game," Ellis said, "but we came back. It was a real good inning for us.
"Both teams really swung the bat really well. We were lucky to get some offense against Lackey. He seems to always get the better end of us, but we were fortunate there."
Suzuki doubled and scored on Barton's hit to tie it in the seventh after the A's had scored twice in the sixth against Darren Oliver.
Matthews' two-out hit gave the lead back to the Angels, but they simply couldn't contain the A's.
"Those guys came back and took it to us," Scioscia said. "It's good on one part -- we scored 10 runs. On the other part, it's uncharacteristic for us to give up that many hits or that many runs."
The Angels seemingly had command when they erupted for six fourth-inning runs highlighted by Bobby Abreu's two-run homer and Chone Figgins' two-run single.
Abreu's blast to right, his 14th, gave him 100 RBIs for the seventh straight season. Only St. Louis' Albert Pujols has achieved that feat the past seven years along with Abreu.
With one swing against A's starter Dana Eveland, Juan Rivera gave the Angels a one-run lead in the first, his three-run bomb to left establishing career season highs in homers (24) and RBIs (86).
The A's had seized the lead in the first on Suzuki's two-run homer, his 15th. Lackey, who took a 16-4 career record against the A's into the game, struggled, yielding three hits and a walk, before escaping.
Cust's 24th homer, an opposite-field blast to left, keyed the four-run fifth, hastening Lackey's exit.
After a four-game run of excellence (three earned runs, 33 2/3 innings), Lackey has given up 10 earned runs in his past 11 innings.
Adam Kennedy doubled home a run in the sixth, his third hit, scoring on a wild pitch by Oliver.
After the A's tied it in the seventh against Jason Bulger on Barton's single and the Angels reclaimed the lead, Cliff Pennington's leadoff double started the decisive eighth.
Jepsen, unleashing 17 consecutive fastballs in the 96-99 mph range, appeared on the verge of escaping after striking out Rajai Davis and Ryan Sweeney behind a walk by Kennedy.
But Suzuki, delivering his fourth RBI of the night, went the other way with a Jepsen fastball to tie it before Cust's double gave the A's the lead.
Barton greeted Palmer with an RBI single before Ellis cleared the decks with his 10th homer of the season, to left field.