The Guardians salvaged their four-game series against the White Sox following a 7-0, shutout win from Chicago.
Logan Allen recovered after getting hit by a line drive in the opening frame and earned the win after pitching six scoreless innings.
David Fry crushed a two-run homer, while Andres Gimenez also went deep.
Estevan Florial recorded a pair of hits to go with an RBI as Cleveland remains first in the AL Central at 25-and-16.