John Danks and the White Sox are focused on catching Detroit and Cleveland in the AL Central. Moving about .500 would be a nice start. Danks pitched six strong innings, Brent Lillibridge hit a three-run homer and the White Sox beat the Kansas City Royals 6-2 on Sunday. Paul Konerko added three hits for the White Sox (60-60), who have won eight of 10 to reach .500. They haven’t had a winning record since they were 7-6 on April 15. Alexei Ramirez had two hits and scored twice as Chicago improved its abysmal home record to 26-33 and moved within four games of AL Central-leading Detroit, which lost 8-5 at Baltimore. The White Sox also won consecutive games in a single series at U.S. Cellular Field for the first time since June 21 and 22 against the Cubs.Danks (5-9) allowed two runs and four hits, struck out six and walked four, improving to 5-1 with a 2.29 ERA in his last nine starts. The left-hander lost his first eight decisions of the season.Jeff Francis (4-13) lasted just 3 2/3 innings for Kansas City, which has lost six of seven. Top prospect Mike Moustakas went 0 for 3 and is 0 for 34 this season against the Sox.The White Sox jumped on Francis in the first inning. Ramirez was hit by a pitch with one out and moved to third on Konerko’s single. Carlos Quentin then hit an RBI single and Lillibridge drove a 1-2 fastball over the wall in left for his 10th homer.Francis has allowed 26 runs in the first inning over his 25 starts this season. Danks was working on a no-hitter before Butler reached on a bad-hop single with two out in the sixth. Butler’s roller down the first-base line hopped up and past Lillibridge. Official scorer Bob Rosenberg originally ruled the play an error, but the call was quickly changed to a hit. Jeff Francoeur followed with a double down the left-field line and Mitch Maier had a two-run single to cut the White Sox lead to 6-2. The White Sox open an important three-game series against second-place Cleveland on Tuesday. They are 6-1 against the Tribe this year.

NOTES—Royals RHP Felipe Paulino is Monday’s scheduled starter against the Yankees. In his last start, Paulino pitched five innings before leaving with a 3-1 lead after 84 pitches due to back stiffness. … White Sox C A.J. Pierzynski missed his third straight game with a bruised left wrist. … White Sox DH Adam Dunn was not with the team for the third straight day to tend to family matters. … Konerko reached base 10 times on 14 plate appearances during the three-game series.