For the second straight time this season, Talbot (7-4) outpitched Peavy. Talbot allowed one run on six hits. He struck out five and walked three.
The rookie right-hander has won all three of his starts against the White Sox with a 1.57 ERA. Talbot held the White Sox to just two runs over seven innings in a win over Peavy on May 25. Talbot threw his first career complete game in a 6-2 home win over Chicago on April 16.
"I felt like just as I was sitting down I was getting up to go back out," Talbot said. "I've enjoyed pitching with him. He works quick and I like to work quick. It's a good mesh for us both."
"The run against Thornton was big because he's almost untouchable," Indians manager Manny Acta said.
With the White Sox quickly falling in the standings, White Sox general manager Ken Williams may go in sell mode, and if he does, Peavy believes he may be one of the players that Williams tries to move.
"I can't get into that, I don't know. It's Kenny's call," Peavy said. "Certainly, I'm one of the guys if he did something that may be something done with. I don't know that's the GM's job and I certainly won't get into that. He can do as he pleases."
Peavy, who initially turned down a trade to the White Sox in last season while with the Padres, waived his no trade clause before last season's trade deadline. Peavy is signed through 2012 with a club option for 2013. He is due $15 million this season, $16 million in 2011 and $17 million in 2012.
Peavy (4-5) pitched seven innings and allowed two runs on six hits. He struck out three and walked one.
"For some reason we pitch very well against these guys, especially Talbot. He's had a few good games against them and we play good defense also. Perez and Woody slammed the door," said Acta.
The White Sox are 1-4 on their nine-game homestand and fell to a season-low nine games under .500. The offensive woes continue for the White Sox, beaten 10-1 by Justin Masterson and the Indians on Friday. Masterson snapped an 11-game losing streak and won his first game since Aug. 20, 2009.
After the game, White Sox manager Ozzie Guillen called his club, "a very bad hitting team."
Peavy was perfect through the first three innings, but was done in with a poor fourth inning. Trevor Crowe and Shin-Soo Choo hit back-to-back singles in the fourth. After a three hit game on Friday, Kearns followed with a RBI single to left. Juan Pierre had trouble picking up Kearns' ball and Choo tried to take third, but was tagged out while sliding into third. Kearns ended up taking second on the throw. During Branyan's at-bat, Peavy threw a wild pitch, allowing Kearns to move to third. Three pitches later, Peavy made a motion to the mound and stopped, resulting in a balk called by home plate umpire Lance Barksdale to score Kearns.
The White Sox had their first crowd over 30,000 since Opening Day. The announced attendance was 30,864. ... Crowe, playing center, made a diving catch on Rios' ball in the seventh inning. ... Travis Hafner broke out of a 0 for 24 slump with a double in the ninth.