It was the hardest contact the White Sox made all day.
The Indians took two of three from Chicago, their second series win this season. They also won two of three against the Kansas City Royals at home April 21-23.
Lee (2-5) hadn't won since the Yankee Stadium opener April 16 and began the day tied for the AL lead in losses despite a 1.70 ERA in his last five starts. The four runs Cleveland scored Wednesday doubled its output in Lee's previous four starts combined.
"He's been about as good as we've seen him. He's been very consistent," Indians manager Eric Wedge said. "He's gone through a stretch here where we haven't scored any runs for him, but he hasn't given in to that."
Lee struck out a season-high nine while working out of two bases-loaded jams and has pitched 20 consecutive scoreless innings against the White Sox dating to July 1. It was the first shutout by Indians pitching this season and already the sixth time Chicago has been blanked.
"They have a good lineup. There's plenty of power there," Lee said. "With a team like that, if you can keep the ball in the ballpark, you're doing a pretty good job."
The reigning AL Cy Young Award winner, Lee allowed six hits -- all bloops, bunts and squibs. Since allowing 11 runs in his first two outings, he has a 1.43 ERA.
"My past few outings have been really good," Lee said. "I feel like I've given the team a chance to win basically every time I've pitched. We haven't gotten those wins, but I feel like I'm doing my job and doing what I can to help the team win. Obviously it's nice to get wins, but I can only control what I can control. That's really all I focus on and everything else I don't worry about too much."
Victor Martinez homered on Buehrle's seventh pitch and Ryan Garko added a two-run shot in the fourth. Garko is 11-for-23 against Buehrle (5-1), who had won five straight starts. He is 9-13 against the Indians.
"He's a strike thrower, and we're a pretty aggressive team," Garko said. "We can run a lot of righties out there against him and a guy in your division you see all the time. He's gotten us plenty of times, but I think seeing him so much, we're more familiar with him."
Three Chicago singles loaded the bases in the sixth, but Lee's strikeout of Dye ended the inning. Dye was ejected after flipping his bat in disgust and slamming his helmet down while arguing with plate umpire Mike DiMuro. The helmet bounced off the ground and hit DiMuro.
Before play resumed, White Sox manager Ozzie Guillen was also ejected by DiMuro for shouting from the dugout. It was the 17th ejection of Guillen's career, the first this season.
"I just told the guy the pitch was low at the knees," Guillen said. "I didn't like the way he was calling strikes and balls. It was kind of weird. I wasn't even adamant about my players. I was adamant about both sides. I think he was a little inconsistent behind the plate."
Chicago again loaded the bases in the seventh, but pinch-hitter Carlos Quentin's soft fly to center ended the threat.
Buehrle lost for the first time since Sept. 24. The four runs were the most he has allowed in a start since Aug. 30, when he gave up seven at Boston.
"I made one bad pitch to Garko," Buehrle said. "Lee's been pitching pretty well and he's had success against us, so you know it will be a tough game."
The last-place Indians open a 10-game, 11-day road trip Friday at Tampa Bay. It is the longest trip of the season for a team that still hasn't won more than two consecutive games all year.
Quentin (sore heel) is expected back in the starting lineup Friday. ... Chicago outfielder Brian Anderson (oblique) is scheduled to begin a rehab assignment with Triple-A Charlotte on Wednesday night. ... Indians DH Travis Hafner (shoulder) is slated to begin a rehab assignment with Triple-A Columbus on Friday. ... Cleveland utilityman Jamey Carroll made his first appearance this season when he started at third base. Carroll opened the year on the disabled list with a broken left hand.