The White Sox erased a five-run deficit on Monday in the opener en route to a 7-6 victory.
Chicago has won three straight over the Royals and remained perfect in Andre Rienzo's last seven appearances on the hill.
Rienzo (4-0) earned the win after striking out eight over six innings, allowing two runs on five hits with two walks.
Tyler Flowers also homered for the White Sox, while Gordon Beckham and Dayan Viciedo contributed an RBI apiece in the win.
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