CHICAGO -- Jon Lester took his manager's advice.
"Sometime, either yesterday or today, (Lester) asked what he had to do," Red Sox manager Bobby Valentine said. "I told him to pitch like an ace. Tonight, he pitched like an ace."
Adrian Gonzalez had an RBI single in the fourth as Lester (1-2) picked up his first win of the season. Lester snapped a career-worst streak of losing five straight decisions and going eight starts without a win dating to Sept. 11 of last season. He gave up five hits and one walk, striking out seven.
"Any win is satisfying, but those games are fun," Lester said. "It's just a battle. I've been on the other end of those. You feel like you do everything you can to put your team in position to win, and the other guy just does a little bit more."
The Red Sox evened their record at 10-10 just a week after a 15-9 loss the Yankees in which they blew a nine-run lead. That prompted Valentine to declare that his team had "hit bottom."
"(A .500 record) is not a goal, but we rebounded off the bottom," Valentine said. "I think we still have a lot of work to do."
Peavy (3-1) failed in his bid to win a fourth straight start for the first time with the White Sox, but threw a complete game for a second consecutive outing for the first time in his career. Peavy hasn't had more than one complete game in a season since 2006, when he was with San Diego.
"I'm giving you all I got," Peavy said. "That's a great team across the way, as you see when Jon Lester puts it all together, he's mighty tough. I wish I could have done a little more to keep that run off the board and give us a chance."
Peavy shut out Oakland on Monday in his last start, a 4-0 win over the Athletics in which he faced four batters over the minimum. He lowered his ERA to 1.67, limiting Boston to four hits, and struck out seven while retiring the last 12 batters he faced.
"Jake's been pitching like that for us all year," White Sox manager Robin Ventura said. "Again, it's unfair for you to expect that out of him every time he goes out, but he just continues to impress and pitch brilliantly."
Alfredo Aceves pitched the ninth for his fifth save in seven chances.
"You play the season to build the little parts of your team," Valentine said. "I think the bullpen is coming together nicely."
Lester had allowed 12 runs over his previous two starts.
Ryan Sweeney hit a bloop double leading off the fourth, the ball falling in after White Sox second baseman Gordon Beckham made a diving attempt for it near the right field line. One batter later, Gonzalez lined a single up the middle to score Sweeney.
"One of my first thoughts is always to try to get the team an early lead," Gonzalez said. "It's big for starting pitchers, so you do whatever you can to get that first run across."
The run ended Peavy's string of 17 straight scoreless innings.
Paul Konerko doubled twice and walked for Chicago, and now has six multihit games over his last eight outings, but it wasn't enough as the White Sox lost their season-high fifth straight.
By winning the low-scoring contest, the win was a departure from the rest of Boston's streak. The Red Sox scored 44 runs over the first five games of the spree.
"That's baseball," Sweeney said. "Everybody is having fun now. I just think we had to get those first few games under our belt. Now we're rolling and we can just keep feeding off each other and keep it going."
In his second rehab start, Red Sox RHP Daisuke Matsuzaka (Tommy John surgery) struck out seven batters in 4 2/3 innings for Double-A Portland. He gave up one run on three hits and walked two. . Konerko's two hits tied him with Eddie Collins for fourth place in White Sox history with 2,007.