With the Brewers leading 3-1 in the seventh, Jean Segura (2-for-4, homer) singled off Michael Stutes, stole second, went to third on a wild pitch and scored on Braun's RBI single to left.
Milwaukee would need the extra run when Philadelphia's Domonic Brown delivered a two-run double in the eighth.
Tyler Thornburg (1-0) earned his first major league victory with two scoreless innings in relief of spot-starter Tom Gorzelanny, who made it through four innings of one-run ball as the Brewers won a second straight against the Phillies.
Philadelphia's Kyle Kendrick (6-4) was reached for three runs on eight hits over six innings.
Brown also cracked a solo homer, his National League-leading 19th of the season.