Straily (9-7) allowed just two hits and one walk while striking out seven in the gem, pitching 67-of-103 pitches for strikes for the American League West-leading A's, who came into the contest with a half-game lead over Texas.
After Dan Otero allowed a run in the eighth, Sean Doolittle closed the door with his first career save as Oakland won for the seventh time in nine games.
Yoenis Cespedes cracked a solo shot in the fourth and Jed Lowrie made it 2-0 with another bases-empty clout in the seventh.
The loss went to Houston's Brett Oberholtzer (4-2), who yielded two runs on seven hits in six innings.
Brandon Barnes provided the Astros' only RBI.
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