Hughes (8-6) controlled the Indians on six hits and a walk, striking out four while locating 74 of his 111 pitches for strikes.
Rafael Soriano picked up his 16th save after Cory Wade surrendered four runs in the top of the ninth, enabling the Yankees to hang on for their fourth straight win and extend their American League East lead over second-place Baltimore to four games.
The Orioles lost 7-3 to the Los Angeles Angels Tuesday.
Stewart's RBI single in the second inning put New York ahead to stay and later adding a sacrifice fly while Curtis Granderson supplied two RBI for the Yankees.
Tribe starter Justin Masterson (7-4) was touched for four runs on seven hits in a six-inning effort.
Jose Lopez cracked a three-run homer for Cleveland.
Swim Week Miami Beach 2014 [PHOTOS]