Trailing 2-0 entering their final at-bat, the O's put runners at second and third with one out thanks to a pair of singles and Athletics pitcher Bartolo Colon's error.
Matt Wieters then chased Colon with a game-tying, two-run double.
Pedro Strop (3-1) earned the victory with a scoreless top of the ninth for Baltimore, which clinched its three-game series with the A's and won for sixth time in seven contests overall.
Colon yielded two earned runs on seven hits over 8 1/3 frames for Oakland.
Seth Smith went 2-for-3 with a solo homer in the loss.
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