Matusz (9-12) fanned eight, allowed three hits and walked two to notch his fifth win in seven starts without a loss.
Markakis broke a scoreless tie with a fifth-inning RBI triple and knocked in the Birds' second run with a seventh-inning single, boosting Baltimore to a victory in the first contest of a three-game series with the Rays.
Wade Davis (12-10) absorbed the loss for Tampa Bay, which maintained a half-game lead over the New York Yankees atop the American League East when the Yankees fell to Toronto 7-5.
Davis yielded three runs on seven hits over 6 1/3 innings.
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