Cabrera's first clout came as the second of back-to-back shots with Quintin Berry in the first inning, handing the Tigers a quick 3-1 lead.
He also connected for another bases-empty blast in the third and Detroit went on to complete a three-game sweep of Chicago, moving 1 1/2 games ahead of the second-place White Sox atop the American League Central.
Brennan Boesch also went deep for the Tigers, who logged their fifth straight win overall.
Rookie Jacob Turner (1-1) earned his first major league victory, surrendering three runs on seven hits over 5 1/3 frames.
Chicago starter Phil Humber (4-5) was touched for six runs on seven hits, lasting only three full frames.