Dunn supplied a solo homer in the third inning and a three-run blast in the fourth, putting the White Sox ahead to stay at 7-5.
The big designated hitter later added an RBI single as Chicago overcame a thick fog that delayed the contest by more than an hour in the third inning and persisted throughout the contest.
Nate Jones (2-4) notched the win with 1 2/3 scoreless innings in relief of starter Dylan Axelrod.
Blue Jays starter R.A. Dickey (5-8) was lit up for seven runs on 10 hits over five full innings.
Jose Bautista smacked a pair of homers for Toronto, finishing with five RBI in the loss.
Colby Rasmus added a solo shot for the Jays.