David Cooper's RBI single in the bottom of the 11th inning sent Toronto past Chicago, 3-2, in the opener of a four-game series.
Jesse Crain retired Rajai Davis on a pop-up to start the frame, then Leyson Septimo (0-2) walked Kelly Johnson before yielding to Nate Jones, who gave up a base hit to Edwin Encarnacion which put runners on the corners.
Cooper stepped in and bounced a single to right which scored Johnson easily to win the game.
It made a winner of Steve Delabar (3-1), who fanned six and didn't allow a hit over two scoreless relief innings.
Encarnacion drove in a run and Moises Sierra added his first career home run for the Blue Jays, who have won two in a row following a five-game losing skid.
Adam Dunn went deep twice for the White Sox, who have lost four of their last six.
"Adam Dunn makes the ballpark look like a little league field every time he steps up to the plate," Blue Jays manager John Farrell said. "That was the case again tonight."
Blue Jays starter Carlos Villanueva scattered five hits and one run with eight strikeouts over seven strong innings, while counterpart Jake Peavy worked eight innings and gave up two runs on five hits, walking two and fanning six.
The Jays picked up a run in the third, as Anthony Gose was hit with one out, went to second when Johnson was plunked, then scored on an Encarnacion single. On the play, Toronto was denied a chance to continue the rally after Johnson was caught in a rundown.
Dunn reached the facing of the second deck in left center with one down in the fourth, but Sierra led off the home seventh with a blast to left and the hosts led by a 2-1 count.
Dunn sliced a ball to the opposite field off Casey Janssen to begin the ninth, tying the game at two.
"We were fortunate enough we had a chance to tie the game and a chance to win it," Peavy said. "They threw some pretty good arms at us tonight and we just came out on the wrong end."
Gose walked with two down in the home 10th, but was caught attempting to steal second to end the inning.
Toronto has won six of its last eight home games against Chicago...Dunn posted his second multi-homer game of 2012 and the 32nd of his career...A.J. Pierzynski extended his hitting streak to 14 games for Chicago.