Granderson collected three hits, including solo shots in the second and fourth inning, and Derek Jeter had two hits, including a two-run double, leaving him four shy of 3,000 for his career.
Robinson Cano, Nick Swisher and Jorge Posada each provided two hits and an RBI for the AL East-leading Yankees, who banged out 17 hits while evening their three-game set with Cleveland at one win apiece.
Sabathia (12-4) became the first major starter to reach 12 wins, striking out 11 batters over seven shutout innings. The Yankees ace yielded five hits and two walks.
Tribe starter Carlos Carrasco (8-5) was rocked for 10 hits over four innings, giving up six runs.
Michael Brantley and Lou Marson drove in the Indians' runs.