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.
The loss went to Addison Reed, but Chicago's pitching struggled throughout the game. Starter Francisco Liriano allowed six hits, five runs, and four walks in five innings of work.
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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