Peavy pitched a three-hitter for his fourth career shutout and the White Sox beat the Nationals 1-0 on Saturday for their season-high fifth straight victory.
"I start every game with the intention of finishing it," Peavy said. "Does that happen very often? Absolutely not. I did what I set out to do today."
Peavy's effort extended a dominant stretch by the White Sox rotation, which is 8-1 with a 1.81 ERA in its last 11 starts.
"Pitching is contagious," Peavy said. "When you watch one guy go out there and do well, you want to follow it up."
Peavy (6-5), whose scheduled start Thursday was pushed back two days because of an achy right shoulder, walked two and struck out seven as the White Sox moved within a game of .500 (33-34) for the first time since April 14, when they were 4-5.
"Coming into the game we didn't know what we were going to get because [Peavy] was having [shoulder] problems," said catcher A.J. Pierzynski, who had three hits. "As the game went on, he got better. He got better and better."
The right-hander, who is 6-1 in his last seven starts against NL clubs, worked out of a two-on, none-out jam in the first and retired 20 Nationals in a row after Roger Bernadina's second-inning single. His previous shutout was Aug. 23, 2005, a 2-0 win for San Diego over Houston.
Carlos Quentin's RBI single in the fourth sent the Nationals to their season-worst sixth consecutive defeat. Chicago has won nine of 10 overall.
"We scratched out just enough offensively to make it happen," Peavy said.
Nyjer Morgan drew a leadoff walk in the Washington ninth and moved to second on Cristian Guzman's sacrifice bunt. Peavy then struck out Ryan Zimmerman looking and intentionally walked Adam Dunn before getting Josh Willingham on a popup to second.
Chicago manager Ozzie Guillen made a visit to the mound before Peavy faced Dunn in the ninth with the tying run at second, but it lasted only seconds. Dunn was 5 for 28 with two homers against the right-hander.
"I don't like to walk the winning run because the baseball gods get you. [Peavy] made a good pitch to the next hitter," Guillen said.
Washington has scored once in 20 innings over two games against Chicago, a trend Zimmerman said has to be reversed.
"Depending on who you're facing, you've got to step your game up and come through with some hits and support our pitchers. They've been throwing the ball well," Zimmerman said. "It's not good to waste performances like that and we need to work a little bit harder and come through in the clutch a little bit more."
Washington starter J.D. Martin scattered eight hits over six innings but remained winless in seven starts since his last victory on Sept. 18, 2009. Martin (0-3) walked none and struck out a career-best six.
"I know what the score is. I know that I need to just keep us in the game," Martin said. "I know [Peavy] is throwing a great game. With a guy like that, it's going to be hard to score runs."
Still, Nationals manager Jim Riggleman isn't pondering any lineup changes.
"I've just got to believe in our guys that we're going to get some pitches, start driving them and hopefully have some men on base when we start doing it," he said.
Chicago improved to 9-2 in interleague play this season, while the Nationals fell to 3-8.
After making a pitching change in the eighth, Riggleman was ejected by plate umpire Sam Holbrook for arguing balls and strikes.
Zimmerman struck out a season-high four times on a day when the Nationals distributed 15,000 bobblehead likenesses of him. ... Vizquel played his 99th straight errorless game. He hasn't made an error since Sept. 14, 2008. Vizquel is not scheduled to play on Sunday when Guillen is expected to give Dayan Viciedo, who was recalled Friday from Triple-A Charlotte, his first major league start. ... The White Sox are the only team in the majors with a winning record (17-16) on the road, but a losing record at home (15-18). ... Chicago has not homered in seven games, its longest skid since April 17-25, 1993, an eight-game drought.