Sabathia (13-3) spent 15 days on the disabled list with elbow inflammation. His showing Friday came as good news for the Yankees as they try to fight off Tampa Bay in the American League East.
Asdrubal Cabrera hit a home run off Sabathia in the fourth inning that created a 1-1 tie, but the New York ace gave up only three other hits in 7 1/3 innings.
Nick Swisher put New York in front with a two-run homer in the seventh and the Yankees went on to hand Cleveland its ninth consecutive loss.
David Robertson came in for Sabathia and recorded the final two outs in the eighth. Rafael Soriano took the mound in the ninth and gave up two singles to open the inning. He then did not allow any of the next three Indians to get the ball out of the infield and wound up with his 32nd save.
Rookie reliever Cody Allen (0-1) gave up the homer to Swisher and his first major league decision became a loss.
New York's lead over Tampa Bay was increased to 3 1/2 games when the Rays fell to Oakland.
2014: The Year in Music [PHOTOS]