KANSAS CITY -- Just when you think Zack Greinke can't possibly pitch any better, he does.

Greinke, the Royals' unsinkable right-hander, floated over the White Sox, 3-0, on a six-hitter Monday night to become the first six-game winner in the Major Leagues. He also leads the Majors in ERA at 0.40 and strikeouts at 54 after adding 10 more. This was his second shutout and third complete game this year.

And it was something else.

"Definitely my favorite game of the year so far, if not ever," Greinke said. "That was a lot of fun."

The 21,843 fans who tramped into Kauffman Stadium on a 68-degree evening certainly thought so. They roared and gave Greinke a standing ovation as he finished off the White Sox.

Why was this game his favorite?

"The biggest difference was probably the fans; they were great today," Greinke said. "And the White Sox were probably the second-biggest reason. It was really a lot of fun."

Yeah, those White Sox have given Greinke some hard times in the past. However, he's won his last three games against them after once standing 2-8. And they were impressed.

"That's the best performance I've seen in a long time by any Major League pitcher," White Sox manager Ozzie Guillen said. "It reminds me when we came here one day and we faced [Bret] Saberhagen and he threw a no-hitter. I think this kid's got better stuff than Bret in that particular time."

Guillen was one of the hitless White Sox in that 1991 no-hitter.

Royals catcher Miguel Olivo has been behind the plate for each of Greinke's victories this season.

"He's got great stuff, man. I think that's the best I've seen Zack throw," Olivo said. "Everything was like perfect. Everywhere I put the glove, he'd hit it."

Greinke started out by retiring the first seven batters, looking like he had no-hit stuff. Then Scott Podsednik got a sharp single just past second baseman Alberto Callaspo. The no-hitter would have to wait.

"I think one day we're going to do it," Olivo said.

However, Greinke did join Saberhagen (1987) and Jose Lima (2003) as the only Royals pitchers to be 6-0 in their first six decisions of a season. Lima won seven before losing.

When David DeJesus drilled a solo home run into the right-field bullpen in the third inning for a 2-0 lead, he already was feeling secure.

"When you see Zack Greinke is pitching, you're like, 'All right, all we have to do is get one or two runs because he's going to be on top of his game right now,'" DeJesus said.

The Royals added a run that inning against Bartolo Colon, as Mark Teahen singled and scored on Billy Butler's single. They had notched an unearned run in the second inning when Jose Guillen singled and came home as Podsednik bobbled Callaspo's single in right field.

The way Greinke was pitching, that was plenty.

A.J. Pierzynski hit a bloop single in the fifth and Podsednik got a double on a bounder that skipped off Butler's glove in the sixth -- nothing very stirring.

Finally, the White Sox stirred in the eighth, when Pierzynski lined a single off Teahen's glove at third and Alexei Ramirez hit a soft single to center. Two on, no outs -- a potential crisis loomed.

"That thought crossed my mind as soon as the next guy came up," Greinke said. "But the next thing I work on is, 'No, it's not going to be big. Just make your pitches. You'll be fine.'"

He made his pitches. Podsednik rolled to shortstop Mike Aviles, who started a double play, although it was not without peril. At first base, Butler had to pluck up Callaspo's low relay throw.

"Billy made the best play of his life," Greinke said. "As soon as Callaspo threw it, it was in the worst spot possible for you to catch it at first, and I was like, 'Dang it, no chance.' But that was a fantastic play."

And then, of course, Greinke struck out pinch-hitter Wilson Betemit to end the inning. And Kansas City manager Trey Hillman sent him back out for the ninth on a night he really didn't want to use closer Joakim Soria anyway.

A fine play by Callaspo started the ninth. Jayson Nix dropped a double inside the left-field line, but Carlos Quentin broke his bat and flied out and Jim Thome popped out.

A shutout was in the books. Greinke has allowed just two earned runs in 45 innings.

"The shutout was not important at all. It was important, though, to let Soria have a day off," he said.

With the crowd roaring, though, Hillman really wasn't thinking about taking out Greinke anyhow.

"I'd like to stick around here for a while," Hillman said. "I figured if I took him out, they'd run me out."