Andruw Jones contributed his 400th career homer and Alex Rios and Dayan Viciedo also went deep for the White Sox, who headed into the All-Star break with an eight-game winning streak and took sole possession of first place in the American League Central.
Royals starter Anthony Lerew (1-3) took the loss after scheduled starter Zack Greinke was scratched due to discomfort in his throwing shoulder.
Lerew was rocked for eight runs on nine hits and a walk in 2 2/3 innings.
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