Toronto had just one hit before breaking through against Aaron Bummer (3-2). José Berríos pitched seven crisp innings in his final start before the All-Star break, and Jordan Romano (4-4) worked the 10th for the win.
Chicago wasted a stellar performance by Lance Lynn, who struck out 11 in seven shutout innings. The White Sox finished with four hits in their fourth loss in five games.
The doubleheader was scheduled after Wednesday night’s game was postponed because of rain.
“Lance was outstanding. We can’t ask for a better start than that,” manager Pedro Grifol said. “He was just outstanding.”
With automatic runner Cavan Biggio on second, Danny Jansen opened the 11th with a dribbler up the third-base line for Toronto's first hit since the third. Springer drove in with Biggio with a grounder back up the middle.
Bo Bichette, Daulton Varsho and Vladimir Guerrero Jr. followed with three more run-scoring singles. Cavan Biggio capped the big inning with a two-run double against Bryan Shaw, lifting the Blue Jays to a 6-0 lead.
White Sox rookie Oscar Colás hit an RBI double and scored on Andrew Vaughn's single in the bottom half. Yimi García replaced Thomas Hatch and got two outs for his first save of the season.
Lynn allowed one hit - Springer's third-inning single - and walked one. The burly right-hander has 41 strikeouts in 25 2/3 innings over his last four starts.
“This has been the worst first half of my career but I’m striking guys out at an elite pace,” he said. "Just got to figure it out how to make it start after start and keep building off it.”
Lynn was matched every step of the way by Berríos, who struck out six and walked one. Elvis Andrus singled in the third for Chicago's only hit off the right-hander.
“Knowing he's going to pitch for them, I know he likes to compete. He likes to pitch long in the game,” Berríos said of the matchup with Lynn. “So I was trying to do my best, trying to pitch quality pitches.”
Berríos got some help from his defense. Springer robbed Zach Remillard of a hit with a diving grab in right for the second out of the third. Alejandro Kirk threw out Andrus when he attempted to steal second after reaching on an error in the sixth.
Berríos threw 64 of his 89 pitches for strikes. He is 7-4 with a 2.80 ERA in his last 15 starts, helping Toronto stay in the playoff race.
“That was my last one (before the break), and I finish really, really strong,” Berríos said.
Chicago placed right-hander Joe Kelly on the 15-day injured list with right elbow inflammation. Nick Padilla was recalled from Triple-A Charlotte, and Jimmy Lambert, another right-hander, was added to the roster as the 27th player.
Toronto added right-hander Jay Jackson from Triple-A Buffalo as its 27th man.
White Sox: 3B Yoán Moncada (lower back inflammation) is expected to begin a rehab assignment after the All-Star break. “He’s doing really well,” Grifol said. Moncada hasn't played in a big league game since June 13. ... Grifol said RHP Michael Kopech (shoulder inflammation) will be available right after the break, and RHP Mike Clevinger (right biceps inflammation) is just a little behind him. “Clevinger, we’re hoping maybe within that week, if not maybe the second week,” Grifol said.
Toronto left-hander Yusei Kikuchi (7-3, 4.08 ERA) and Chicago right-hander Jesse Scholtens (1-2, 2.96 ERA) start the second game of the doubleheader.
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