But then they lost 16 of 21 games, and now they're fourth in the American League Central.
Greinke held a 4-1 lead after three innings, which, in his first 10 starts this season, would have been enough to win. He had not given up more than two runs in any game to this point. However, he couldn't hold back the White Sox.
"I couldn't finish 'em off," Greinke said. "They got base hits with two strikes and two outs. And that's usually what I feel like I'm real good at -- when you need just one more out, I could finish it off. But today they beat me in that situation."
A prime example took place in the fourth inning, when Jim Thome, who singled, and A.J. Pierzynski, who doubled, were parked at second and third with two outs. Greinke got ahead of Josh Fields with a 1-2 count. But Fields grounded a single right up the middle for two runs that brought the White Sox back into the game.
After being beaten twice and held scoreless for 15 innings by Greinke previously this season, the White Sox decided on an aggressive approach. They decided to go up swinging.
"Because he's been striking so many people out, to put the ball in play was almost a victory," Fields said. "I think the more balls we put in play, the luckier and the more of a chance we had."
By the fifth inning, Greinke already had thrown 92 pitches, and getting his sixth complete game was out of the question. The White Sox got their fourth run in that inning on Scott Podsednik's double off the right-field fence and Jermaine Dye's looping single.
"He wasn't as sharp as he usually is," catcher Miguel Olivo said of Greinke. "He left a couple sliders flat, but other than that, he pitched good. That team right now is getting hot. They're hitting and winning games [eight of the past 11]."
After that, though, Greinke threw two perfect innings and left after seven with the score tied at 4. One of the White Sox runs was unearned, but his Major League-leading ERA puffed up to 1.10 from 0.84. But Greinke did increase his string of innings without giving up a home run to 110, the longest since Kevin Brown's 118 innings in 1996-97.
Greinke gave up eight hits, matching a season high, but walked none and struck out seven. You have to go all the way back to Sept. 13, 2008, against the Indians for the last time he gave up at least three earned runs in a game.
"I just really wasn't finishing guys off when it had to be done," Greinke said.
There was a bad sign when Podsednik began the game with a triple to left-center field.
"Podsednik -- if I could get him out, it'd be a lot better," Greinke said. "He always does that to me. I probably threw him about 40 pitches today, too."
Although Greinke almost escaped by fielding a comebacker and then striking out Dye, the right-side shift was foiled by Thome, who grounded a single through the vacant shortstop hole. Podsednik loped home.
The Royals stormed back against left-hander John Danks in the second inning on singles by Mark Teahen and Olivo and David DeJesus' two-run double to left-center. DeJesus also scored when Mitch Maier's high popup, the apparent third out, was missed by circling shortstop Alexei Ramirez as he squinted into the bright blue sky.
"I think it got in the sun. That's a tough play when he's got to run back and battle the sun," Maier said. "That's why you run hard. I was lucky to get to second."
Maier got a double and the Royals got a 3-1 lead. They added a run in the third on Mike Jacobs' double and Olivo's single.
After the White Sox attained the tie, the game marched into the ninth inning. That's when they conjured up three runs against the Royals' bullpen.
John Bale gave up a one-out bloop single to Pierzynski and Brian Anderson. Juan Cruz relieved Bale and walked Fields to load the bases. Chris Getz lined a single to deep right field for two runs, with Fields thrown out at third on the play while Getz reached second. Podsednik popped his third hit, a single that scored Getz for the third run.
In the end, there was admiration for Greinke, but not enough runs to bring him a victory this time.
"A starting pitcher's job is to give you an opportunity to win a ballgame, and he certainly did that today," Royals manager Trey Hillman said.
"It was an unusual number of runs scored off him and an unusual number of hits in comparison to what he's done in the rest of his starts. But he's still got great stuff."