Ryan Raburn tied the game with a two-run homer winner two batters later in the bottom of 8 victory over Chicago in game set.
Luis Marte (1-0) tossed a scoreless top of the ninth to earn the win. Brad Penny started and allowed eight runs -- four earned -- on 10 hits and a walk in five innings for Detroit, a winner in four of its last five games.
"Every game is huge, every win is huge," Cabrera said. "We have to go out there and try to finish the job."
The Tigers hold a 6 1/2-game lead on Cleveland in the AL Central.
Sergio Santos (3-4) allowed the game-deciding runs in the ninth to take the loss. Gavin Floyd allowed four runs on eight hits through five innings in his start for Chicago. He did not issue a walk and struck out four.
"You feel like you let the 24 other guys on your team down," Santos said. "They busted their tails and played really well, so to go in there and mess up that one inning, it's tough."
After a Delmon Young strikeout, Cabrera launched a first-pitch, low-and-inside slider into the seats in left, capping an eight-run comeback. The White Sox held an 8-1 lead after five innings.
An A.J. Pierzynski sacrifice fly to left brought home Ramirez from third in the top of the first, but the Tigers answered with a Cabrera RBI double off the top of the wall in right in the home half.
Chicago tacked on five runs in the fourth, which Dayan Viciedo and Alex Rios began with back-to-back singles. Two batters later, an error by Tigers second baseman Carlos Guillen allowed Brent Morel to reach, filling the bases. Gordon Beckham followed with a base hit to right, scoring Viciedo.
Juan Pierre then hit a grounder to first. Cabrera fielded the ball and threw to home for the force out, but Alex Avila's throw back to first was wide and Morel was able to score on the throwing error. Ramirez then pulled a ball over the left-field wall, putting the White Sox ahead 6-1.
Back-to-back solo homers by Alejandro De Aza and Morel in the fifth extended Chicago's lead.
But Detroit began to fight back in the bottom of the fifth. Jackson's triple brought Guillen across the plate, and Young's shot into the left-field bleachers made the score 8-4.
Chicago activated pitcher Philip Humber off the 15-day disabled list Saturday...Detroit has won 17 of its last 23 games vs. Chicago...Jackson extended his hit streak against Chicago to 14 games...Cabrera has reached base safely in 30 straight games.