Justin Upton smacked a two-run homer, while Freddie Freeman and Ryan Doumit added solo shots for the Braves, who recorded a season-high 15 hits. Mike Minor (2-2) allowed two runs on five hits and two walks over 6 2/3 innings to notch the win.
Khris Davis cracked a two-run blast and Ryan Braun stroked a solo homer for Milwaukee, which has dropped two in a row. Wily Peralta (4-3) surrendered three runs -- two earned -- on nine hits and four walks over five frames in defeat.
The Brewers cut into a 3-0 deficit by plating a pair in the fifth. Mark Reynolds worked a leadoff walk and Davis launched a two-run shot into the seats in left-center.
Atlanta got a run back in the sixth. After Minor and Heyward singled against Zach Duke to begin the frame, Upton reached on catcher's interference to load the bases with none out. Freeman struck out, but Evan Gattis lifted a sacrifice fly into right against Rob Wooten to bring Minor home and make it 4-2.
Braun got Milwaukee back within a run with one out in the eighth after he smacked an 0-2 fastball that just crept over the wall in right.
Atlanta, however, broke the game open in the bottom half after pushing across five runs against Wei-Chung Wang. The pinch-hitter Doumit belted his 100th career homer into left and Upton cracked a two-run blast into the seats in right to extend the margin to 7-3. Andrelton Simmons and Ramiro Pena added RBI singles later in the frame to make it 9-3.
Atlanta raced out to its three-run cushion after plating a run in each of the first three frames.
Heyward singled to begin the first and stole second before scoring later on a passed ball. Pena's RBI single in the second and Freeman's leadoff opposite- field shot that glanced off the glove of Davis' in the third made it 3-0.