A Ben Gamel two-run home run in the 5th inning was not enough to silence the White Sox.
Eloy Jiménez answered quickly for the White Sox in the 6th inning to tie it all up 2-2 and a single from José Abreu allowed Danny Mendick to score and keep the lead 3-2.
Chicago has now won six straight, all on the road.
The Brewers now head to Chicago for a two game series against the White Sox. Adrian Houser is set to start for the Crew and Dallas Keuchel is set to start for the White Sox.