Chicago scored seven times over the first three innings, making things easy for starter Hector Santiago.
Santiago (3-5) gave up three hits and a run over eight innings. He benefited from an 11-hit Chicago attack that allowed the White Sox to end a three-game losing streak. The Royals have dropped three straight.
Chicago scored twice in the first on a bases-loaded walk to Paul Konerko and a sacrifice fly by Conor Gillaspie.
The White Sox then sent eight men to the plate in the third and everyone who reached base in the inning scored.
Bruce Chen replaced Guthrie and Viciedo hit Chen's second pitch over the wall in left.
Guthrie (7-5) suffered the loss, allowing six runs on five hits in 2 1/3.
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