Kansas City, Mo. ? The last thing the slumping Kansas City Royals needed was for Mark Buehrle to get even better.

But the Chicago left-hander tinkered with the grip on his sinker and became even more dominant than usual against the Royals, taking a four-hit shutout into the ninth before settling for a 4-1 victory that gave the surging White Sox their sixth win in a row.

“I had everything working,” said Buehrle (8-2), who raised his career mark against Kansas City to 20-8. “I changed my sinker grip in the bullpen because the last two or three games, it’s been cutting instead of sinking. So I moved my fingers closer together, and I think it was probably one of the best sinkers I’ve had in a while.”

Buehrle failed to get his first complete game since May 2, 2008, when Alberto Callaspo doubled and scored on David DeJesus’ one-out double. He was relieved by Bobby Jenks, who got the last two outs for his 19th save in 21 chances for the White Sox, who have won 10 of 12 and 14 of their last 19 on the road.

Until the ninth, the 30-year-old Buehrle had been dominant. He did not issue a walk and had a season-low one strikeout in 81/3 innings. He threw 68 strikes in 100 pitches.

“That’s kind of embarrassing to get only one strikeout,” he said. “But it’s good to put the ball in play early and go deep in games. I’ll take this every time, obviously.”

Mark Teahen, one of the few Royals hitters who seems to have much luck against the 30-year-old Buehrle, was 2-for-3, raising his career mark against him to .440.

“I asked him if he’d sign (the ball),” Buehrle said with a grin. “I finally got him out.”

Teahen grounded out in the eighth.

“He’s tough. He really is,” Teahen said. “He mixes up all his speeds, pitches both sides of the plate. You want to be selective with the guy. But when he’s pounding the strike zone, throwing all his pitches for strikes, it’s hard to be too patient.”

Jayson Nix hit a solo home run off Bruce Chen (0-2) as the Royals lost their sixth in eight games. They’ve scored only three runs in their last three games, all losses.

Chen went six-plus innings plus two batters and gave up two runs on five hits. Making his second major-league start since undergoing Tommy John surgery in 2007, Chen walked one and struck out five and did not allow a hit until Nix hit a 2-2 pitch out leading off the fourth.