The Sox, who have won 13 of their last 16 games, have a commanding 5 1/2-game lead over second-place Toronto and a magic number of five to clinch the American League East. Baltimore, losers in six of eight games at home, remained in third place and is tied with Detroit for the second AL Wild Card spot, pending the Tigers' game Thursday night.
Boston chased Baltimore's Opening Day starter, Chris Tillman, from the game after five outs -- the ace's shortest start of the year -- jumping out to an early lead three-run lead. Price, who allowed all three of his runs on rookie Trey Mancini's homer, held firm from there, as Boston added a run in the fifth and Hanley Ramirez went deep in the seventh inning.