Braun's solo shot in the fourth tied the score 1-1 and his two-run blast in the fifth put the Brewers up 5-2.
He added another bases-empty homer and capped his big night with a two-run three-bagger in the ninth.
Randy Wolf (2-2) earned the victory, surrendering three runs on nine hits in a five-inning start while walking three and striking out three.
Padres starter Joe Wieland (0-4) struck out eight over five innings but yielded five runs (three earned) on five hits and lost his fourth straight start.
Yonder Alonso went 2-for-3 with an RBI for San Diego.