The Royals had pulled out to a 5-3 lead in the 6th, but Chicago short stop Alexei Ramirez tied the game at five with a two-run homer moments later.
Kelvin Harris picked up his eleventh win of the season, while Greg Holland converted his twelfth save this year.
Kansas City will face the White Sox in Chicago again on Saturday in the second of a three game series. Chicago maintains a half game lead over the Detroit Tigers in the AL Central.
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