Chicago has won four of its last five games after getting swept by the Yankees last weekend.
White Sox starter Dallas Keuchel allowed four runs on eight hits in five innings to get the victory.
Evan Marshall pitched a perfect sixth inning and Liam Hendriks threw a perfect seventh for his 11th save.
Baltimore starter Matt Harvey struggled again. He allowed five runs on five hits and three walks.
Freddy Galvis homered twice and Maikel Franco hit a solo shot for the Orioles, who have lost 11 straight games.