With the score tied 2-2 in the ninth, Dayan Viciedo hit a leadoff single against Aaron Crow (3-3) and John Danks came in to run for him. After Crow issued a walk to Jeff Keppinger, Greg Holland took the mound and pinch-hitter Gordon Beckham moved Danks to third on a deep fly to right-center.
De Aza followed by lining a pitch to Royals right-fielder Jeff Francoeur, whose throw home was high and not in time to catch a sliding Danks for the go-ahead run.
Jesse Crain (2-1) earned the decision with a scoreless eighth and Addison Reed picked up his 21st save for the White Sox, who clinched their three-game series.
Mike Moustakas went 2-for-4 with an RBI double and Salvador Perez drove in a run for Kansas City.