Brett Hayes added a solo shot for the Royals, who closed out a positive season with an 86-76 record.
Bruce Chen (9-4) allowed just one run on four hits over 6 2/3 innings and Greg Holland survived a shaky ninth inning for his 47th save.
Jose Quintana (9-7) yielded four runs on six hits over seven innings for the White Sox (63-99).
Alexei Ramirez homered for Chicago.
Celebrity Breakups and divorces of 2014 [PHOTOS]