Eloy Jiménez went deep in his second straight game, helping the White Sox end a series that was shaping up as a bad one for them on a stronger note.
The reigning AL Central champions rolled into the break by winning three of four at division-leading Minnesota. They hoped this series against the second-place Guardians would help keep pushing them toward the top.
Cleveland lost its second in a row after winning five straight.
Bieber got tagged for six runs and eight hits in six innings. The 2020 AL Cy Young Award winner tossed a three-hitter in a 4-1 victory over the White Sox in his previous start on July 12.