With Ronald Belisario (3-4) on the mound for Chicago in the ninth with the White Sox holding a 4-3 lead, Steve Pearce singled and Adam Jones was plunked with no outs. Belisario struck out Nelson Cruz, but Davis entered the game to hit for Delmon Young and crushed a slider over the wall in right for the win.
Caleb Joseph and Jones both homered earlier and Young finished 3-for-4 for Baltimore, which has won three straight and five of its last six.
Brad Brach (1-0) earned the win after not allowing a hit across the eighth and ninth innings. Orioles starter Wei-Yin Chen gave up three runs on six hits and two walks in 5 2/3 innings of work.
Jose Abreu homered among his two hits and drove in three runs for the White Sox, who lost their fifth straight game and eighth consecutive road contest. Starter Chris Sale gave up two runs and a career-high 11 hits in six innings.