Getting the start on the mound, Davies fanned two White Sox hitters.
After trailing most of the game, the Brewers tied it 5-5 in the top of the seventh inning. Manny Pina hit an inside-the-park homer, and Troy Stokes mashed a three-run dinger to left field.
But the White Sox responded with four runs of their own in the bottom half of the frame, rolling to the 9-5 win.
Tyler Saladino tallied two hits, two runs scored and an RBI in the loss.
Milwaukee hosts the Arizona Diamondbacks on Friday afternoon.