A solo shot by Davis in the fourth put the Orioles in front 2-1, but Chicago tied it when Gordon Beckham produced a homer in the fifth.
Davis put Baltimore back in front in the eighth with his two-run double than ran his RBI total for the season to 83.
Baltimore won for the fifth time in six games.
The loss went to Matt Lindstrom (2-3), who retired only one batter in the eighth. It was the sixth White Sox loss in seven games.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Beyonce flaunts bikini body, Blue Ivy in vacation pics