With the White Sox trailing 2-0 in the fifth inning, De Aza drove in A.J. Pierzynski with a two-out single and Dewayne Wise followed with a ground ball up the middle to drive in Dayan Viciedo and send De Aza to third.
Blue Jays starter Henderson Alvarez (7-10) then tried to pick off Wise at first base but threw the ball away, allowing De Aza to come home with the decisive run.
The rally made a winner of Jose Quintana (5-2), who held Toronto to a pair of runs on eight hits over 6 2/3 innings. The left-hander walked two and fanned four.
Brett Myers and Matt Thornton combined for an inning of scoreless relief and Addison Reed notched his 21st save for the American League Central-leading White Sox, who evened their four-game series at one win apiece.
Alvarez yielded three runs (two earned) on seven hits over seven frames.
Mike McCoy and Yunel Escobar drove in runs for the Blue Jays.