Dickey (2-2) allowed two hits, both singles. The reigning NL Cy Young Award winner, walked one, struck out a season-high seven and lowered his ERA from 5.82 to 4.30.
Dickey retired the first 11 White Sox batters before Alex Rios hit a two-out single to center in the fourth. Rios went to second on a wild pitch and Paul Konerko walked, but Adam Dunn struck out to end the inning.
Blue Jays trainer George Poulis and manager John Gibbons came to the mound after Dickey struck out Dewayne Wise for the second out of the sixth. After a brief discussion, Dickey remained in the game, getting Jeff Keppinger to fly out to left.
Dickey appeared to be rubbing his upper back as he left the dugout and walked to the clubhouse at the end of the inning.
Esmil Rogers pitched 1 1-3 innings, Aaron Loup got two outs and Casey Janssen finished for his fifth save.
Davis led off the first with a single and stole second and third on consecutive pitches before scoring on Edwin Encarnacion's two-out hit to left.
Toronto added two more runs in the fifth. Emilio Bonifacio was hit by a pitch and went to third on an errant pickoff throw by White Sox left-hander Chris Sale. One out later, with the infield drawn in, Bonifacio scored when Dunn couldn't handle a grounder by Munenori Kawasaki.
The White Sox spoiled Toronto's shutout bid in the eighth. Alexei Ramirez chased Rogers with a one-out single and scored when Tyler Flowers hit a two-out double off Loup. Wise grounded out to end the threat.
Sale (1-2) gave up a career-high eight runs in his previous start on Sunday at Cleveland, but was sharper in this one. He allowed three runs, two earned, and four hits over seven innings. He walked one and struck out six.
Sale is 2-7 with a 5.83 ERA in his past nine road starts going back to last season.
White Sox outfielder Dayan Viciedo left in the eighth with apparent soreness in his left side after swinging and missing on a pitch from Rogers.
Blue Jays slugger Jose Bautista missed his fourth straight game with a sore back. Blue Jays manager John Gibbons said Bautista is "showing progress" and could return Friday against the New York Yankees.
NOTES: Toronto RHP Sergio Santos will not throw for seven days after an MRI confirmed a strained muscle in his throwing arm. Santos was placed on the 15-day DL Monday, retroactive to April 14. ... White Sox OF Alejandro De Aza got the day off. ... Attendance was 18,015.