The teams split a four-game series with Dickey (2-2) turning in a seven-strikeout performance with one walk.
Casey Janssen recorded a 1-2-3 ninth to collect his fifth save.
Edwin Encarnacion delivered a two-out, RBI single in the first inning for the Blue Jays and Toronto added two runs in the fifth thanks to a series of Chicago miscues.
White Sox starter Chris Sale hit Emilio Bonifacio with a pitch to start the inning, then made a wild pickoff attempt that allowed Bonifacio to make it all the way to third.
Chicago first baseman Adam Dunn compounded the problems by committing a fielding error on a grounder from Munenori Kawasaki. That allowed Bonifacio to score and Kawasaki soon came in on a double from Rajai Davis.
The lone Chicago run scored on a double by Tyler Flowers in the eighth.
Sale (1-2) allowed the three runs, two of which were earned, on four hits over seven innings.