Fiers (3-2) baffled the Diamondbacks on two hits and three walks, lowering his ERA to 2.29 over his seven major league games, including six starts.
Braun's second-inning solo blast opened the scoring and put Milwaukee ahead to stay. His two-run homer in the fourth capped a six-run Brewers uprising.
Cody Ransom added a three-run clout en route to four RBI as Milwaukee evened its three-game series at Miller Field.
D-backs starter Wade Miley (9-4) was rocked for eight runs on eight hits, lasting only 3 2/3 innings.
Miguel Montero went 2-for-4 with a solo homer for Arizona.