CHICAGO (AP) Brent Lillibridge hit a three-run homer, John Danks pitched six strong innings and the Chicago 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. Alexei Ramirez had two hits and scored twice. 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 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) is 5-1 in his last nine starts after starting the season with an 0-8 record.