Chris Carter had a two-run double as part of a five-run third inning while Josh Reddick added two hits and an RBI for Oakland, which has won two straight over Baltimore to clinch the season series between the top two teams in the American League wild card race.
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Parker (11-8) allowed two runs and seven hits over seven innings to win back-to-back starts for the first time since mid-July. The A's rookie right-hander struck out five, walked one and retired 11 of the final 13 batters he faced.
Sean Doolittle pitched a scoreless eighth and Grant Balfour worked the ninth for his 19th save.
Drew, obtained in a trade from Arizona on Aug. 20, provided a spark with both his bat and glove.
His home run off Baltimore starter Zach Britton was the first of four hits in the inning by Oakland in the third. It's Drew's second home run as a member of the A's and fourth overall.
The A's shortstop then made the first of his two defensive gems when he threw out Adam Jones trying to score from first on Chris Davis' double in the fourth.
Jones reached on a leadoff infield single and Davis followed with a double down the left field line. Jones kept running as Yoenis Cespedes retrieved the ball and threw it to Drew, who turned and made the relay throw home just in time to nab Jones as he was attempting to slide past catcher Derek Norris.
Oakland third baseman Josh Donaldson made a stellar defensive play of his own with two outs in the fifth when he caught McLouth's foul ball while leaning over the rolled-up rain tarp near the stands.
The win moved the A's a season-high 23 games over .500. Oakland (84-61) has already won 10 more games than it did last year.
Baltimore took an early 2-0 but couldn't make it hold up.
The Orioles managed only two hits after the fourth inning and stranded a pair of baserunners in the ninth when Balfour got Chavez to ground to third for the final out.
Parker got the Orioles to ground into a double play in the first but his error on a pickoff attempt in the second led to Baltimore's first run.
Jones singled and was leading off the bag when Parker's throw to Carter at first base went in the dirt and rolled almost to the Orioles bullpen. Jones raced to third then scored on Reynolds' double to left.
McLouth made it 2-0 with his third homer of the season that hit off the facing above the scoreboard in right field. It's only the ninth home run allowed this season by Parker.
Britton (5-3) didn't allow a hit until the third when the A's scored five runs.
Drew's solo home run started the outburst. After Rosales grounded out, Coco Crisp walked before Britton hit Jonny Gomes on his left elbow to put runners at first and second.
Reddick and Cespedes both followed with RBI singles, and Carter doubled both men home to make it 5-2.
Britton gave up five earned runs for the second consecutive start. The left-hander had four strikeouts and four walks.
Notes: Baltimore has hit into five double plays in the first two games of the series. ... Rookie RHP Dan Straily (2-0) pitches for Oakland in the series finale. ... LHP Randy Wolf (2-0) makes his first start since signing with Baltimore after being released by Milwaukee in late August.