KANSAS CITY -- For the better part of the next three weeks, the White Sox will not play a game more than 90 minutes away from U.S. Cellular Field.

When factoring in the three Interleague contests against the Cubs from June 16-18 at Wrigley Field, 15 of these 18 matchups on the schedule will take place in Chicago.

And the White Sox are coming home with more than a little momentum.

Chris Getz's bases-loaded single off reliever Juan Cruz with one out in the ninth completed the White Sox improbable comeback for a 7-4 victory and three-game series sweep of the Royals on Sunday afternoon at Kauffman Stadium. Improbable, only in the fact that the Royals held a 4-1 lead with Zack Greinke on the mound, which usually is the equivalent of the slaughter rule behind the closest pitcher to unhittable in the game this season.

Greinke did not pick up his Major League-leading ninth victory, and he did not beat the White Sox for the third time in three 2009 starts. In fact, the White Sox scored four runs off Greinke, the most the right-hander has allowed in any of his 11 starts this season, skyrocketing his ERA all the way up to 1.10.

After watching his team complete a 5-1 road trip and win for the ninth time in 12 games, White Sox manager Ozzie Guillen was most impressed with the way his lineup attacked the Royals' immovable pitching force.

"I think the approach at the plate every hitter had was outstanding, facing the best in the game, making him throw that many pitches," said Guillen, whose patient offense drove up Greinke's pitch count to 114 through seven innings. "We made him throw a lot of pitches.

"That kid, believe me, when he had to throw big pitches with men on base, he was outstanding. When you see Greinke there, you want to get to the bullpen. Everyone in baseball thinks the same way. It's not that their bullpen is bad, but that kid is so good, you don't want to see him on the mound."

Kansas City's bullpen was not particularly sharp during Sunday's fateful ninth inning, after Jamey Wright fanned Paul Konerko to start the frame. A.J. Pierzynski's bloop single down the left-field line off left-handed reliever John Bale (0-1) began the game-deciding rally, giving Pierzynski his third hit of the game. Pinch-hitter Brian Anderson walked, and Cruz promptly issued a walk to Josh Fields upon replacing Bale.

Getz rifled a 2-1 pitch up against the right-field wall, bringing home Pierzynski and Anderson. Fields was thrown out at third on the play, meaning Getz only was credited with a single. Regardless of the semantics, Getz provided a resounding shot from the bottom of the White Sox order, following Fields' two-out, two-strike single off Greinke in the fourth to bring in two runs and cut the deficit to 4-3 at the time.

Getz's two RBIs gave him four for the three-game series, with this weekend breaking his 21-game RBI drought in May.

"I'm glad May is over," said a smiling Getz, who left in the bottom of the ninth with a sore right foot that was not deemed any sort of problem by the White Sox. "With that being said, there were still a lot of positives to take out of it.

"During the second half of May, we started doing well. Personally, I was battling some stuff, but that's part of the whole deal for rookies. It's how you answer back, and something like this can carry a little momentum."

Kansas City (23-27) took early control with three runs in the second off John Danks. Two of those runs scored on David DeJesus' double, with DeJesus then scoring when shortstop Alexei Ramirez lost Mitch Maier's popup and it fell for a double.

Danks finished with a no-decision, as Matt Thornton (2-1) picked up the win and Bobby Jenks recorded his 12th save. Danks gave up four runs on nine hits over 5 1/3 innings, striking out five, but needing 100 pitches to get the job done.

"He fought like a champ," said Guillen of the southpaw starter. "He gave the team the best chance to be close in the game."

Fields' two-run single brought the White Sox close, and Jermaine Dye's fifth-inning single scored Podsednik with the tying run. Podsednik finished a home run short of hitting for the cycle, but more importantly, worked Greinke to a three-ball count in each of his first three trips to the plate.

Series sweep chances existed for the White Sox against each of their past three opponents in Minnesota, Pittsburgh and Los Angeles. This sweep situation seemed to play out as the toughest.

Instead, the White Sox (24-25) picked up their first road sweep since May 16-18, 2008, in San Francisco, and their first sweep at Kauffman Stadium since April 22-24, 2005. Now, they return home for a season-high 12-game homestand, looking to reach .500 for the first time since they were 12-12 on May 3.

With the weather expected to heat up, matching the White Sox bats, and the Tigers coming in for a five-game set next week, .500 might only be the starting point for this team.

"When the White Sox play in the middle of the summer at home, it should be a good time," White Sox hitting coach Greg Walker said. "We should play well. But you've got to do it. Saying it and making it happen are two different things.

"Our goal really is just to take one day at a time and then we can look back and say we played pretty well over a particular stretch. You just can't look too far forward."