The Jays took a 12-8 lead into the ninth inning but Chicago got three runs off reliever C.J. Wilson before he struck out two batters to end the contest.
Jermaine Dye had a home run, a double and three RBI, Orlando Cabrera drove in three runs and Carlos Quentin homered for the White Sox.
Jamey Wright (6-4) was the winning pitcher, giving up a run in a 1 2/3 innings.
Boone Logan (2-2) was charged with the loss after pitching to three batters and being charged with three runs in the seventh.
Celebrity Families of 2014 [PHOTOS]