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.
Susan Sarandon 'very excited' about daughter's pregnancy
Dennis Rodman pledges to end trips to North Korea