Dustin Pedroia and Ross broke a 1-1 tie with back-to-back doubles against Luis Ayala (5-5) to produce the decisive run.
But Boston had to hang on in the bottom of the ninth to preserve the win, which enabled it to avoid a three-game sweep.
The O's loaded the bases with one out against Andrew Bailey, but he retired Manny Machado on a force-out at home and struck out pinch-hitter Ryan Flaherty to rack up his sixth save.
Junichi Tazawa (1-1) retired the Orioles in order in the eighth to earn the victory.
Machado got the only RBI for second-place Baltimore, which stayed one game behind the American League East-leading New York Yankees despite the loss.