The game was delayed at the start by rain, which did nothing to dampen the White Sox offense.
Adam Dunn hit a two-run homer in the first inning and Chicago then sent 10 men to the plate in the fourth on its way to a second straight victory.
Dunn started the big inning with a walk against Jeanmar Gomez (2-2), moved to second on a single by Paul Konerko and came in on a base hit from A.J. Pierzynski. A walk to Alex Rios loaded the bases and Alexei Ramirez drove in a run with a single.
Jake Peavy (4-1) gave up only a seventh-inning run on eight hits with one walk and five strikeouts to pick up the victory.
Gomez allowed all eight runs over 6 2/3 innings.
Celebrity Families of 2014 [PHOTOS]