Winning pitcher Kameron Loe (7-4) surrendered two runs and four hits over six innings with one walk and three strikeouts.
Paul Konerko hit a run-scoring double for the White Sox, who have dropped four of five. Their lead over Cleveland dropped to 6 1/2 games in the American League Central Division.
Loser "El Duque" Hernandez fell to 8-7. He gave up six runs and six hits over five-plus innings with one walk and six strikeouts. Hernandez, who has not won in his last five starts, fell to 5-3 on the road this season.