Cabrera tied the score at 6 with a three-run shot. Conor Gillaspie homered early for Chicago, its first long ball since April 22.
Victor Martinez homered and knocked in four runs for the Tigers.
Chicago trailed 6-3 in the eighth after Martinez drove in his fourth run of the night with a single.
Victor Martinez's two-run homer broke a 1-all tie in the third. He drove an 0-2 pitch from Chris Sale into the left-field stands.
Chicago tied it in the fourth on Melky Cabrera's sacrifice fly.
Detroit took a 1-0 lead on Victor Martinez's sacrifice fly that scored Davis, who led off the game with a triple.
The White Sox pulled even in the second on Gillaspie's first home run of the season. The solo shot snapped a nine-game home run drought for Chicago.
Tigers: SS Jose Iglesias returned to the lineup after leaving Sunday's game against Kansas City with tightness in his left groin. Iglesias was scheduled to return Tuesday, but was a late scratch by manager Brad Ausmus. ... RHP Justin Verlander was cleared to start throwing and made about 50 throws Wednesday in the outfield. Verlander has been sidelined all season with a strained right triceps and underwent a third MRI exam Tuesday.
White Sox: Relief pitcher Nate Jones will remain in Chicago through the weekend so the White Sox can determine the next steps in his rehabilitation. Jones had Tommy John surgery last June and has been at extended spring training. Jones, on the 60-day disabled list, said the message from manager Robin Ventura and pitching coach Don Cooper is to remain patient and focus on getting through each day healthy.
Quintana allowed nine earned runs and 10 hits in four innings during his last outing against the Tigers on April 19.