Bumgarner (5-1) has earned victories in each of his last five starts following an April 7 loss to Arizona. The left-hander limited the Brewers to one run on six hits, issuing only one walk while fanning five.
Buster Posey and Hector Sanchez each collected an RBI in the victory.
Milwaukee starter Randy Wolf (2-3) was touched for four runs on nine hits in a six-inning effort.
Ryan Braun homered for the Brewers, who fell for the third time in four games.