Parker pitched seven innings of three-hit ball, Brandon Moss and Cliff Pennington homered, and the A's snapped the Angels' six-game winning streak with a 3-1 victory Monday night.
With his second straight impressive start against Los Angeles after a hard-luck loss last week, Parker (10-8) and his bullpen held the Angels' surging lineup to four hits. Parker beat the Angels for the first time in his career by going right at Albert Pujols, Mike Trout and Mark Trumbo, holding Los Angeles to one run for only the second time in its past 22 games.
''They were aggressive as well, so I tried to get some early contact, early outs,'' Parker said. ''It's fun. These are the kind of starts that we need, and everybody is going to feed off this kind of energy.''
Coco Crisp hit a leadoff triple and scored for the A's, who opened a key four-game series against their California rivals with a measure of revenge for the Angels' three-game sweep in Oakland last week. Those are the only losses since Aug. 23 for the A's, who have won 13 of 16.
''It was definitely a big game for us,'' Pennington said. ''They came into our place and did what they needed to do, so we needed to come in here that way. This was a good start. Right now, every game is huge. There's one or two differences in every game.''
Ryan Cook worked the eighth, and Grant Balfour finished uneventfully for his 17th save.
Dan Haren (10-11) pitched into the seventh inning, allowing just four hits and striking out four. But Oakland turned those hits into three runs, and Haren took his first loss since Aug. 16.
Torii Hunter drove in Trout with a third-inning double for the Angels (77-64), who had won 11 of 12 and 15 of 18 in their desperate late surge to join the playoff race.
''I'm not surprised anymore at what they're doing,'' Hunter said of the A's. ''I mean, we were surprised when they first started doing it in early August, but I'm not surprised any more. They're playing the game, and they've got some really good arms over there.''
With its first home loss in seven games, Los Angeles blew a chance to pull within a half-game of Baltimore (78-62) for the second AL wild-card spot. Tampa Bay (77-63) is between the Orioles and the Angels.
Oakland (80-60), which is in the first wild-card slot, is 20 games over .500 for the first time since the end of the 2006 season — also the year of the team's last postseason appearance. The A's pulled within three games of idle Texas (83-57) atop the AL West.
''Nothing really surprises me in baseball anymore after the way last season finished, and with the way the Orioles and A's are playing this year,'' Haren said. ''We're getting to the point where they're not going away, so it's going to be a fight to the finish and the better team is going to win.''
Crisp hit Haren's first pitch of the night high off the right-field wall, easily reaching third before scoring on Seth Smith's groundout. Oakland didn't lead at any point in last week's three losses to the Angels, who outscored the A's 21-5 in the East Bay.
Trout and Hunter evened it in the third inning when Trout walked, stole second, advanced on an error and trotted home on Hunter's double down the right-field line.
Hunter was greeted each inning in right field by a long row of fans wearing fluorescent-yellow T-shirts and holding up signs spelling ''Keep Torii!'' The beloved outfielder can become a free agent this winter.
Haren retired 12 straight A's on just 38 pitches after Crisp's triple, but Moss led off the fifth with his 17th homer. Pennington added his fifth of the season in the sixth inning, also reaching the elevated stands above right field.
NOTES: Angels manager Mike Scioscia said ace Jered Weaver will start Thursday against the A's after skipping a start to rest the tendinitis in his right shoulder. Weaver, who felt strong after a bullpen session Monday, would be lined up to start the Angels' final game of the season if he returns Thursday. ... Jerome Williams gets a spot start in Weaver's place when the Angels face the A's on Tuesday night. Oakland counters with Dan Straily, who will make his fourth major league start in Brandon McCarthy's slot in the rotation. ... Los Angeles reliever Nick Maronde gave up a single to Moss after relieving Haren in the seventh. Maronde, a third-round pick in 2011, had struck out each of the first four batters he faced in his major league career since getting promoted from Double-A Arkansas on Sept. 1.