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.
Millions of Getty images now available for free via embed tool
Boston schools pull out free condoms over wrapping complaints