KANSAS CITY -- It could seem unfair, this 4-1 loss that wasted a gem from Mark Buehrle and a moon shot from Jermaine Dye. But when you consider what happened the last two nights, perhaps the Royals were due.

Chicago toyed with Kansas City twice in a row, falling behind, 5-0, on Tuesday and, 4-1, on Wednesday before breaking the Royals' hearts in the end on both nights. This time, the White Sox had the lead and seemingly everything going right, but it was Kansas City which came back.

The Royals finally figured out starter Mark Buehrle in the eighth, and Chicago relievers allowed two doubles and a crushing inside-the-park home run to Mark Teahen. When it was over, Kansas City had pushed four runs across, and well, so much for the sweep.

"Everything happened so quick," Buehrle said. "I was kind of going out there pitching good. Seemed like in five seconds we were down, 4-1, and we lose the game."

The loss was Chicago's first to Kansas City this season, after winning their first five games against the Royals. The Sox defeat, combined with Minnesota's comeback win, means Chicago now sits 2 1/2 games ahead of the Twins.

The eighth inning got off to a rough start, as Paul Konerko dropped a ball at first base that would have completed a double play. David DeJesus was safe on the error.

"On a double play," Konerko said, "Sometimes when you have to reach out, that kind of makes it tough. But whatever, the play wasn't made."

The next batter, Mike Aviles, ripped a double down the left-field line, scoring DeJesus and tying the game at 1. Octavio Dotel then entered the game and retired Mark Grudzielanek before Jose Guillen doubled to center field, scoring Aviles.

The final blow came when Teahen sent another shot toward center field, this one off Boone Logan, that reached the wall. Guillen easily scored, and Teahen went for the inside-the-parker after second baseman Alexei Ramirez hesitated before throwing the ball home. Teahen barely beat the throw.

Dotel and Logan were each charged with an earned run. On Tuesday, Scott Linebrink gave up two runs and blew a save. Chicago fans must be begging for Bobby Jenks' return right now.

"Bullpen's been beat up," manager Ozzie Guillen said. "I got a couple guys out, and we tried to take care of them the best we can."

Buehrle's runs were unearned due to the error, but he took the loss.

In his last outing, against the A's, Buehrle talked of not being able to find his stuff. His pitches were up, and he couldn't get ahead in the count. Buehrle didn't make it out of the sixth inning, and gave up four runs and 10 hits. The loss snapped a four-game winning streak, and was nothing like his June performances.

Buehrle's June magic returned on Thursday, as he struck out four of the first six batters. He continued to cruise until that eighth inning. In total, he went 7 1/3 innings, striking out a season-high eight batters.

Royals starter Zack Greinke matched him, giving up one run in seven innings. It was a big run though, a shot from Dye that looked like it was going to reach Saturn.

Dye went hitless in 10 at-bats in the first two games of the series and struck out against Greinke in the first inning on Thursday. He snapped out of it in the fourth inning Thursday, however.

Greinke's first pitch was a fastball, and Dye rocked it above the fountains in left field, sending the ball 434 feet onto a small green platform that few, if any, balls ever touch.

But that was about all the White Sox could do against Greinke. He dazzled, something that might've been somewhat unexpected given his 2-7 record against Chicago before Thursday.

Not once did the White Sox get more than one baserunner in any of his seven innings, and Greinke struck out eight.

"To me," Guillen said, "he is one of the best pitchers in the American League."