Winning games is the bottom line for Jake Peavy. As strong as his pitching has been, he still wants to improve.

Peavy pitched his second straight complete game but was outdueled by Jon Lester and the Red Sox bullpen as the White Sox lost 1-0 to Boston on Saturday night — Chicago's fifth straight defeat.

The former Cy Young winner was masterful again, limiting a Red Sox offense that had scored 20 runs in the first two games of the series to just four hits and one run.

Peavy (3-1) struck out seven and walked one, retiring the last 12 batters he faced to lower his ERA to 1.67.

"It's just frustrating to lose," Peavy said. "I'm at the point in my career where I want to win. My team wanted me to do a little bit more than I did, it just didn't happen."

The only blemish came in the fourth inning. Ryan Sweeney led off with a bloop double down the right-field line, just beyond the reach of a charging Gordon Beckham.

After Dustin Pedroia lined out to third, Adrian Gonzalez sent a 2-2 pitch though the infield to plate the only run of the game.

"I just have to make a better pitch to Gonzalez there," Peavy said. "I made good pitches to him most of the night. You make a mistake to him and he's gonna make you pay, and he got on top of a ball that ran back to the middle and got a big hit for them."

Peavy 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 start for the first time in his career. He hasn't had more than one complete game in a season since 2006, when he was with San Diego.

Peavy shut out Oakland on Monday in his last start, a 4-0 win in which he faced four batters over the minimum.

The run ended Peavy's string of 17 straight scoreless innings.

The White Sox offense couldn't get going against Lester (1-2), who made big pitches when he needed to. Chicago went 0 for 6 with runners in scoring position and stranded eight on base.

"You can look back and see little things, you had opportunities," White Sox manager Robin Ventura said. "You tip your hat to Lester for getting out of those situations.

"Any time he got into a bind, he found a way out of it."

Lester picked up his first win of the season, snapping a career-worst streak of five straight losses and going eight starts without a win dating to Sept. 11. He gave up five hits and one walk, striking out seven.

"Sometime, either yesterday or today, he asked what he had to do. I told him to pitch like an ace," Red Sox manager Bobby Valentine said. "Tonight, he pitched like an ace."

Lester had allowed 12 runs over his previous two starts.

The Red Sox won their sixth straight to even their record at 10-10 after a miserable start.

Franklin Morales and Vicente Padilla held the White Sox scoreless in the eighth. For Morales, it was his 22nd straight scoreless road outing, most ever by a Boston left-hander.

Alfredo Aceves pitched the ninth for his fifth save in seven chances.

The low-scoring 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.

Paul Konerko doubled twice and walked for Chicago, and now has six multi-hit games over his last eight outings.

NOTES: 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. ... LHP Andrew Miller (hamstring) gave up a two-run homer and struck out three in one inning of relief for Triple-A Pawtucket. ... Konerko's two hits tied him with Eddie Collins for fourth place in White Sox history with 2,007.