Dayan Viciendo's grand slam highlighted a five-run fourth inning as the White Sox dealt the Royals their fourth straight loss by a final of 5-2. Kansas City (64-61) has now dropped seven of their last nine since starting the second half 19-5.
It's the third straight loss for Guthrie (12-10), who gave up nine hits and struck out a pair through six innings.
Kansas City's runs came on a fourth-inning sacrifice fly from Mike Moustakas and a sixth-frame RBI single by David Lough.
James Shields takes the mound against Jose Quintana in the series finale on Thursday.