Instead the club is playing the role of spoiler and has done just that against contending teams, winning eight of the last 12 against the White Sox, Orioles and Athletics in the last two weeks.
The Royals are hoping to continue the trend as they go for the sweep of the White Sox at Kauffman Stadium on Sunday.
If starter Jeremy Guthrie continues his recent strong stretch, the White Sox may not be able to reverse their woes. The right-hander is coming off two straight wins, his first since May 31.
In his most recent start, on Tuesday against Oakland, Guthrie threw seven shutout innings, giving up just three hits and two walks to go along with eight strikeouts. He had success against the White Sox in the start prior to that one, going eight scoreless innings, allowing just five hits and fanning six.
His opponent, Jose Quintana, has been no slouch himself lately. He's coming off two straight starts in which he allowed a pair of runs in each, winning one and losing the other.
Against Toronto his last time out, he allowed those two runs on eight hits and two walks to go with four strikeouts in 6 2/3 innings. He got enough run support to edge out a 3-2 win over the Blue Jays.
The White Sox haven't given their pitchers much run support against the Royals recently, scoring just 13 runs in the last five matchups.
White Sox: Stiff back sidelines De Aza
Outfielder Alejandro De Aza was pulled for a pinch-hitter in the eighth inning of Friday's matchup against the Royals, and a stiff back forced him to the bench on Saturday.
Manager Robin Ventura said there is a strong possibility that De Aza will be unable to go on Sunday.
Dewayne Wise got the start in center field and went 1-for-4 at the dish.
Paul Konerko, in the lineup as a designated hitter on Saturday in his second game back after dealing with a concussion, is expected to play first base on Sunday.
Royals: Giavotella looks to make most of chance
With second baseman Chris Getz on the disabled list for the rest of the year with a fractured thumb, the Royals are looking to Johnny Giavotella to fill the void.
The 25-year-old Giavotella is in his second stint with the Major League club but struggled in the first, batting .217 with six RBIs in 21 games (15 starts). He's fared well in the Minors though, hitting higher than .320 in each of the last three seasons.
"I feel terrible for Getz. I hate to come up at the expense of his health," Giavotella said. "But at the same time, I'm happy I'm getting the opportunity. I'm going to make the most of it and help the team win."
Giavotella started on Saturday, going 0-for-4 with a pair of strikeouts.
Getz underwent successful surgery on his thumb on Saturday, manager Ned Yost said.
Chicago has lost eight of its last 11 in Kansas City and nine of 17.
Konerko and Adam Dunn are the first teammates in Major League history to hit their 400th career home runs in the same season. Dunn reached that milestone in the eighth inning of Saturday's game; Konerko accomplished the feat in April.