Guthrie (1-0) allowed five hits and one walk and wasn't in much trouble until the fifth when the Royals were already up 3-0. One day after the White Sox hit four home runs in beating the Royals, all of Chicago's eight hits Thursday were singles,
Greg Holland turned in a one-hit ninth for his first save.
Kansas City managed just five hits -- four off Gavin Floyd (0-1) over six innings -- but three were bunched together for a three-run rally in the top of the fifth.
Eric Hosmer walked with one out in the fifth and Jeff Francoeur followed with a single. Hosmer scored on a fielder's choice and Francoeur reached home on a Chris Getz single. Alex Gordon followed with a double that made the score 3-0.
A hit-by-pitch and consecutive singles, the second by Alejandro De Aza, gave the White Sox their run in the bottom of the inning.