He'll try to duplicate that performance Tuesday night when he makes his return to Chicago as the Boston Red Sox open up a three-game series.
Peavy (0-0, 2.13 ERA) went 36-29 in parts of five seasons for the White Sox before being sent to Boston as part of a three-team deal prior to last year's trade deadline. He limited Chicago to two runs over seven innings of a 7-2 home victory for Boston on Aug. 31.
Tuesday will mark Peavy's 43rd game at the White Sox's home park, but his first as a visitor.
"It will be strange. We enjoyed having him here and he was a good pitcher," Chicago manager Robin Ventura told the team's website. "I'm sure the guys will have fun. They will try to do something to distract him, I'm sure."
Peavy is without a decision through his first two starts while limiting opponents to three runs over 12 2-3 innings. He struck out eight in 6 2-3 innings in Wednesday's 4-2 comeback win over Texas.
The Red Sox (5-8) might need a stellar showing from Peavy given their offensive struggles. They lost three of four to the Yankees in New York while totaling 11 runs and 27 hits. Eight of those runs came from homers as Boston was 4 for 24 with runners in scoring position, dropping its average to .204 in such situations. The Red Sox were third in the majors with a .278 average with runners in scoring position in 2013.
Dustin Pedroia was scratched from Sunday's 3-2 loss and was set to have his sore left wrist examined in Boston on Monday. Pedroia has one RBI on the season and has gone 3 for 27 (.111) while leaving 17 runners on base over his last six games.
"I think there's probably a direct correlation to what we've seen at the plate," manager John Farrell said.
Jonathan Herrera started at second base in place of Pedroia while Xander Bogaerts occupied his usual No. 2 spot in the order. Each went 1 for 4.
The White Sox (7-6) took three of four at home against Cleveland with Alexei Ramirez going 7 for 16 with six RBIs in the series. He hit a walkoff two-run homer in Sunday's 4-3 victory, and is 21 for 50 (.420) on the season while collecting at least one hit in all 13 games.
"Everything is about the preparation, I believe," said Ramirez, who is batting .321 over his last 20 matchups with Boston. "You know, this year I've been working on that and being prepared. I have my routine and, obviously, things have been good."
Conor Gillaspie has also hit safely in 11 games he's played, batting .341 with nine RBIs.
Adam Dunn, who is 5 for 11 with two doubles in his last three games, is just 5 for 31 off Peavy with 11 strikeouts.
Chicago will start Erik Johnson (0-1, 9.58), who has never faced the Red Sox or any of their current hitters.
He's been inefficient in two starts, throwing 205 pitches spanning 10 1-3 innings. The right-hander was charged with four runs and nine hits over 5 2-3 innings in a 10-4 loss at Colorado on Wednesday, but didn't receive a decision.
Boston has taken 12 of 16 in the series dating back to July 30, 2011, and won last season's series 4-2.
David Ortiz hit .381 with eight RBIs versus Chicago in 2013.