The Brewers were behind 2-1 in the fifth inning when they put two runners aboard with two outs against Cubs starter Scott Feldman (0-3), whose fielding error kept the inning alive.
That brought up Braun, who smashed a 2-2 offering into the upper deck in left field, boosting the Brewers to a three-game series sweep of Chicago.
The blast handed a first major league victory to Wily Peralta (1-1). The Dominican rookie surrendered a pair of runs on five hits over 6 2/3 frames, walking three and striking out three.
Jim Henderson turned in a scoreless ninth for his fourth save as the Brewers moved above .500 (9-8).
Feldman was touched for four runs (one earned) on three hits over five full frames.
Anthony Rizzo went 2-for-4 with a two-run clout for the Cubs, who fell for the sixth time in seven games.