Vazquez (6-4) allowed five hits and two runs in seven innings.
The Yankees broke a 2-2 tie with a seventh-inning rally. Miguel Cairo singled and advanced on a sacrifice by Bubba Crosby. After Derek Jeter was hit by a pitch and Alex Rodriguez sruck out, Gary Sheffield doubled in two runs and Hideki Matsui singled in another.
John Parrish (3-2) was the loser.
The win, New York's eighth straight over Baltimore going back to last season, gave the Yankees a sweep of a three-game series.
2014: The Year in Music [PHOTOS]