"That's the way we should play every day," Lee said. "With that kind of intensity."
Courtney Duncan capped a wild opener in the crosstown series, saving the Sox in front of a crowd of 45,936, the largest in the 10-year history of new Comiskey Park.
"It was mentally draining, exhausting," White Sox manager Jerry Manuel said. "You had to be in on every pitch."
The win was the 12th in 14 games for the Sox, while the loss was the Cubs' second in their last 17 games. The Cubs remained five games ahead of second-place St. Louis in the National League Central, while the Sox picked up a game on Cleveland, moving to 11 1/2 games behind the Indians.
With one out in the 10th, Duncan walked Tony Graffanino and gave up an opposite field single to Chris Singleton. A wild pitch moved the runners over, and Cubs manager Don Baylor ordered an intentional walk to Ray Durham to load the bases. Duncan fanned Magglio Ordonez before Lee took hold of an 0-1 slider and cranked it into the left-field bleachers.
The Cubs had several opportunities, but stranded 11 runners against seven Sox pitchers.
"The ballgame was decided when we didn't take advantage of men in scoring position," Baylor said. "We couldn't get the ball in play enough."
Sox starter David Wells suffered through the shortest outing in his career, committing two throwing errors and failing to retire any of the five batters he faced before leaving with back spasms.
"I've never had one that was that severe before," said Wells, who had been dealing with a sore groin. "I'm figuring out a lot of things. First the groin, now this."
Wells was in the unfamiliar position of pitching in front of a packed house at Comiskey and appeared to be as nervous as a rookie. Leadoff hitter Eric Young laid down a perfect bunt which Wells fielded cleanly before bouncing a throw past first base, allowing Young to advance. Miguel Cairo bunted to move Young over, but Wells lobbed another weak one-hop throw that eluded the mitt of first baseman Paul Konerko and resulted in Wells' second error.
Lee's run-scoring single off ex-Sox starter Jason Bere got the Sox on the board in the first, and a sacrifice fly by Graffanino tied it at 2 in the fifth. Graffanino had replaced Jose Valentin at third after Valentin aggravated his right hamstring.
Matt Ginter hit Julio Zuleta with the bases loaded in the seventh to put the Cubs up 3-2, but Sandy Alomar Jr. tied it in the bottom of the inning with an RBI single.