Oakland climbed within three games of Texas for the lead in the American League West with five to go and stayed two games in front of the Los Angeles Angels for the AL's second wild card berth.
The Athletics will play their final five contests at home, the last three against Texas.
Trayvon Robinson homered for Seattle in the second inning to forge a 1-1 tie, but Drew gave the A's the lead one inning later. Oakland broke it open with a four-run seventh that featured a two-run single from Josh Donaldson.
A.J. Griffin (7-1) started for the A's and bounced back from his lone loss of the season. He gave up a run on four hits in 5 2/3 innings, during which he threw 96 pitches.
Blake Beavan (10-11) was tagged with the loss after he allowed three runs on four hits in 4 2/3.