Kyle Schwarber hit a two-run homer in the sixth inning as the Cubs won for just the fourth time in their last 11 games.
The NL Central leaders were outscored 17-5 in the first two games of the series.
Jose Abreu went deep for the White Sox in the second, matching a major league record with a home run in four consecutive at-bats.
Abreu connected five times in the first two games against the Cubs, including three homers and four RBIs in Saturday night's 7-4 win.
ABREU HITS 3 HRS, 5 IN 2 DAYS; CHISOX TOP CUBS, 7TH W IN A ROW