Dunn and Viciedo hit two of the game's five home runs to break open what had been a 4-4 contest.
The division-leading White Sox won their second straight after letting an early four-run lead get way.
Toronto tied it in the sixth on a three-run homer by Kelly Johnson, but Chicago stormed back in front during the next half inning.
Alejandro De Aza drew a leadoff walk off Ricky Romero (8-10), who then hit Kevin Youkilis with a pitch. Brad Lincoln came on to replace Romero and Dunn promptly hit Lincoln's third pitch over the wall for his 34th homer of the season.
A.J. Pierzynski followed with a one-out double and, with two away, Viciedo hit one out to right.
Gavin Floyd (9-9) lasted six innings to get the victory, giving up four runs on eight hits with eight strikeouts and no walks.
Exploding whale video goes viral on Internet
Wisconsin business offering 'therapeutic cuddling' forced to close