Lester fanned eight and became just the 10th different Boston pitcher to reach the 200-strikeout plateau.
"Strikeouts are nice. A cool stat," Lester said. "That's not something I'm trying to do. It's something I'll look back on after my career and realize it's pretty cool."
After losing Friday and Saturday to the White Sox, Boston increased its AL wild-card lead to three games over Texas, which lost to Baltimore 7-0.
"Even when Lester fell behind he was able to come back and throw strikes. Seven strong innings," Lowell said. "He's been solid for us all year. This was a big start, especially after the way the first two games went."
Lester (12-7) has struck out 204 this season. It marked the 24th time overall a Red Sox pitcher has reached 200 strikeouts. Daisuke Matsuzaka did it two years two years ago.
"He's just got great stuff," Chicago's Paul Konerko said. "Throws hard, good cutter, curve when he needs it, he threw me a couple of changeups. Just mixed it up and pitched really well and didn't really have a pattern it seemed like."
Chicago had won four in a row. The loss dropped the White Sox eight games behind AL Central leader Detroit with only 24 games left.
"The way Detroit is playing right now, they are on a roll and we're not," White Sox manager Ozzie Guillen said. "It's not impossible, but every day will be tougher, even if you win or you lose."
Boston added a run for a 3-0 lead in the fifth. Jacoby Ellsbury beat out an infield single and moved up on sacrifice and, after Kevin Youkilis was hit by a pitch, Bay delivered a RBI single with two outs.
Ramon Castro homered leading off the White Sox eighth against reliever Billy Wagner.
But Martinez hit a three-run shot off Octavio Dotel in the ninth, his 21st homer of the season and sixth since joining the Red Sox on July 31.
The White Sox put runners on in three of the first four innings but could not break through against the hard-throwing Lester. Lester threw 122 pitches, has won his last four decisions and hasn't lost since July 19.
"I got myself in some trouble, but made some pitches when I had do. I got some outs when I got myself in jams," he said.
Danks lost his bid for a career-high 13th win and pitched in and out of trouble most of the day in the matchup of tough left-handers. In six innings, he gave up seven hits and three runs.
"You know going up against a guy like that you got to be almost flawless," Danks said of Lester. "He's a guy who every night will give you a chance to win. He's going to hold a team to a run or two. ... I got outpitched."
Chicago's first two batters reached in the first. But with his back to the infield, Boston second baseman Dustin Pedroia raced into shallow right to make an over-the-shoulder catch of Konerko's fly. He then turned and threw to second to double off Scott Podsednik.
"Pedroia didn't get any hits, but he probably saved the game in the first inning," Red Sox manager Terry Francona said. "At best we're looking at bases loaded and nobody out because I think everybody in the ballpark thought the ball is falling."
- Ellsbury had three singles and a walk.
- Chicago rookie Gordon Beckham, who hurt his side Saturday with a batting practice swing, was out of the lineup after starting 65 straight games at third base. Beckham, who left after a half-inning Saturday, is expected to also miss Monday's series finale.
- Chicago's Alex Rios struck out three times. Rios, claimed off waivers from Toronto last month, is in a 4-for-46 rut over his last 12 games.