Brown finished 3-for-3 with four RBI while Erik Kratz added an run-scoring double and Freddy Galvis chipped in with an RBI triple during the early five-run outburst.
Cliff Lee (7-2) rode the big inning to his fifth win in six starts, yielding three runs on seven hits over 7 2/3 innings.
The left-hander didn't issue a walk and struck out 11 while lowering his ERA to 2.45 as the Phillies salvaged the final contest of a three-game set.
Milwaukee's Mike Fiers (1-4), meanwhile, didn't make it out of the second inning. He was torched for seven runs (five earned) on seven hits.
Jonathan Lucroy clouted a three-run homer homer for the Brewers.