For the second time this season, Zack Greinke held Chicago scoreless while allowing six hits in the Royals' 3-0 victory Monday.

Looking for a season-high fourth consecutive win overall, Kansas City (15-11) has won three in a row over the White Sox after taking the final two games of their season-opening series at Chicago last month.

With a 3.72 combined ERA, Kansas City's rotation is among the best in the American League. Gil Meche, Greinke and Davies have been particularly stingy against Chicago (12-13), which looks to avoid a season-high fourth straight defeat.

That trio has combined to allow one run - off Meche in the second inning of a 4-2 loss on April 7 - in 29 innings over four starts against the White Sox. Chicago is batting .192 with 31 strikeouts against them. The club also has been shut out four times this season, twice by Kansas City.

Davies (2-1, 4.85 ERA) allowed three hits and struck out eight in seven scoreless innings, but didn't factor in the 2-1 win over the White Sox on April 9.

The right-hander, who is 2-2 with a 4.46 ERA in six starts versus Chicago, gave up three runs and seven hits in 5 2-3 innings of an 8-6 victory over Toronto on Thursday.

"I felt like I threw the ball really good," said Davies, who benefited from six double plays turned behind him. "The ball came out of my hand the best it probably has all year. The location wasn't the best."

David DeJesus homered and Billy Butler also drove in a run Monday for the division-leading Royals, who are also trying for a fourth consecutive home victory.

DeJesus is batting .253, but is 7-for-17 with five RBIs in his last four games. He's hitting .313 (5-for-16) with a home run against Chicago's scheduled starter Gavin Floyd.

Floyd (2-2, 5.52) is 1-4 with a 3.62 ERA against the Royals, and allowed two runs and six hits while striking out nine in seven innings of a 2-0 loss on April 8.

In his most recent start, the right-hander allowed three runs and 10 hits in six innings, but did not get a decision in a 6-3 win over Seattle on Wednesday.

"I felt like I battled and did pretty well," Floyd told the White Sox official Web site.

A.J. Pierzynski and recently acquired outfielder Scott Podsednik each had two hits Monday for the White Sox, who have been outscored 8-1 in their last two games.

Chicago's lineup could get a boost if Jermaine Dye returns after missing two straight games since getting hit on the hand with a pitch Saturday in Texas.

"Hopefully (he) will be ready to play," manager Ozzie Guillen said of Dye, a former Royal who is 7-for-16 in his last four games against Kansas City.