The Indians were trailing 4-3 in the sixth when Lonnie Chisenhall drew a lead-off walk from Tim Collins (2-5) and Drew Stubbs followed with a single.
After Michael Bourn laid down a sacrifice bunt to advance the runners, Cabrera (3-for-5) laced a 1-0 pitch into the right-center field gap for a two-run two-bagger.
Jason Kipnis then added an RBI single and the Tribe went on to take a fourth straight win overall and remain 1 1/2 games behind American League Central-leading Detroit at the All-Star Game break.
Carlos Santana went 3-for-3 with an RBI in the triumph.
Rich Hill (1-1) got the decision after retiring the final two batters of the sixth and Chris Perez picked up his 13th save for the Tribe.