CLEVELAND -- Showing up somewhere between 45 minutes to one hour late for Wednesday afternoon's series finale at Progressive Field would have cost a fan about five innings in Cleveland's 4-0 victory over the White Sox.

There's no room for tardiness when Mark Buehrle and Cliff Lee, two of the American League's top left-handed starters and quickest workers, get the call. Unfortunately for the White Sox, their offense didn't officially show up until the sixth inning.

And even at that point, sitting in a four-run hole, it was really just a brief appearance.

Lee (2-5) pitched out of bases-loaded, two-out jams in both the sixth and seventh innings, extending his scoreless innings streak thrown against the White Sox (15-18) to 20 straight. Lee improved to 6-5 against the South Siders and 3-1 in pitching matchups with Buehrle (5-1).

Most of the credit for this series-deciding victory goes to the 2008 American League Cy Young Award winner. The White Sox lack of offensive punch also deserves a mention, as they finished with their Major League-high sixth shutout of the 2009 campaign.

"I don't want to take any credit away from him, but we didn't exactly give him the best fight," said White Sox first baseman Paul Konerko, who had one of the seven hits off of Lee. "We fought, but I don't think it was our best game.

"At the same time, he threw a lot of counts where it could have gone either way, a 1-0 or 2-0 count where you're kind of going, 'OK, here we go,' and then he painted a strike. He made the pitch when he had to, not down the middle, but on the corner, and that's why he had a good day. I know [his] win-loss [record] isn't where he wants it to be, but his ERA is pretty good and that's usually a pretty good barometer."

The biggest outburst from the White Sox came in the sixth inning, and it had little to do with swinging the bats. In fact, it was a called third strike taken by Jermaine Dye on a 2-2 pitch with the bases loaded that set off the fireworks.

Dye instantly disagreed with home-plate umpire Mike DiMuro's call, and when he slammed down his helmet, DiMuro gave Dye his third career ejection and first since May 21, 2007. The arguments didn't stop there.

After Jhonny Peralta took a called third strike to open the bottom of the sixth, White Sox manager Ozzie Guillen complained from the dugout about DiMuro's strike zone once again. Guillen picked up his 17th career ejection, this one coming strangely in support of the opposition.

"[DiMuro] got a little confused because he had never seen that in his life, a manager arguing for the opposition," Guillen said. "I didn't like the way he was calling strikes and balls and I went to argue.

"This argument was weird because I wasn't even arguing about my players. I was arguing about both sides. Sometimes you just shake your head about what's going on and meanwhile, you're the one who got tossed. I got to pay the fine and we move on. You're not going to win this one, but I got to do what I got to do. I think he was a little inconsistent behind the plate."

Aside from a handful of bad pitches, Buehrle featured the consistency Guillen sought from DiMuro. Victor Martinez launched his seventh home run of the season with two outs in the first, while Ryan Garko added a two-run, two-out shot off of Buehrle in the fourth.

Garko is 11-for-22 lifetime against Buehrle. It was that pitch to the Cleveland designated hitter, along with a leadoff walk issued to Matt LaPorta leading to a run in the fifth, which rankled Buehrle the most during his first loss in seven starts. Much like facing Buehrle, whose ERA rose to a still-solid 3.00 after giving up four runs on seven hits over seven innings, there isn't much room for error when facing Lee.

"A lot of people are saying he doesn't have much run support," said Buehrle, who struck out six and walked one. "He's a great pitcher and he's had success against us, so you try to go out there and throw up zeros but I made one bad pitch to Garko and the leadoff walk to LaPorta. I won't say I'm mad about those things but I wish I could have those back."

"He's a strike thrower, and we're a pretty aggressive team," said Garko of Buehrle. "That's a part of it. We can run a lot of right-handers out there against him. He's a guy in our division who we see all the time. He's gotten us plenty of times, but we're definitely more familiar with him."

Consistent offensive production is something the White Sox have not been all too familiar with during the first six weeks of the 2009 season. Guillen believes his team is striking out too much, adding 10 more against Lee, Rafael Betancourt and Kerry Wood.

According to Konerko, it's an overall problem easy to identify and to critique from the outside but not easily fixable.

"Let's think about it, if you said enough is enough, what's that going to do?" Konerko said. "You never go into a game expecting bad things, so anything verbal or any of that rah-rah stuff, it just doesn't cut it in this game.

"Adding intensity doesn't amount to success. It's a matter of very fine things that need to happen for a hitter to do well or a team to do well. It's not just about wanting it sometimes. Everybody wants it, everybody tries their best."