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.