Danks (2-5) held the Orioles to two runs on six hits, breaking a personal three-start losing streak. The left-hander walked two and struck out four en route to the triumph.
Addison Reed hurled a scoreless ninth inning for his 22nd save as the White Sox snapped a four-game losing streak in the opener of a three-game series.
Conor Gillaspie's solo homer in the sixth broke a 1-1 tie and Adam Dunn added a two-run shot in the next frame to ice the victory.
Baltimore's Jason Hammel (7-5) was tagged with the loss, surrendering five runs on nine hits over seven full frames.