Cleveland ended a five-game losing streak with a power display while the Orioles lost their third in a row.
Damon hit a three-run homer in the fourth, Choo lifted a solo shot in the fifth and Cabrera produced a three-run blast in the seventh.
Baltimore's runs came on a homer by J.J. Hardy in the fifth.
Zach McAllister (2-1), called up Thursday to begin his second stint with the Indians this season, lasted 5 1/3 innings to get the win. It was his second victory in nine major league starts scattered over two seasons.
McAllister allowed the Hardy homer and six other hits while striking out six.
Wei-Yin Chen (7-4) suffered the loss, giving up six runs on six hits in 6 1/3 innings.