Anderson (3-1) cruised through the first six innings, mixing a 96 mph fastball, an effective changeup and an even slower curveball that kept the Brewers guessing.
The 23-year-old right-hander walked four and struck out four before the Brewers ended Anderson's bid in the seventh. Daniel Vogelbach blooped a leadoff single to center and Pablo Reyes followed with a double that chased Anderson.
Reliever A.J. Minter gave up a sacrifice fly to Luis Urías.
Anderson helped the Braves win their fifth straight road game and match their longest road winning streak over the last three seasons.
Milwaukee has lost 10 of 13 and slipped to 20-20 this season.
Freeman homered in the second. William Contreras homered off Hoby Milner leading off the Atlanta eighth.
Travis Shaw was called out on strikes to end the Brewers fourth. He turned to bark at plate umpire Chris Segal who listened briefly and then tossed him. Reyes.
The Braves jumped on a shaky Brett Anderson (2-3) for a 4-0 lead.
Ozzie Albies doubled home Freeman, and Dansby Swanson followed with a sacrifice fly in the first. Freeman capped the second with his 10th home run.
Braves: OF Ronald Acuña Jr. missed his second consecutive game after injuring his left ankle while trying to beat out a grounder on Thursday against Toronto. Manager Brian Snitker said that Acuña made some progress.
Brewers: OF Christian Yelich continued a rehab assignment with Triple-A Nashville on Saturday night. "Every day’s a little bit more," manager Craig Counsell said. "We’ll see how he reacts to it." Yelich was hitless in two at-bats Friday night. The 2018 NL MVP has played just one game for Milwaukee since April 11 due to a lower back strain.
BRAVES ROSTER MOVES
The Braves returned OF Guillermo Heredia from his rehab assignment, reinstated him from the 10-day injured list (right hamstring inflammation) and started him in center field. … INF Johan Camargo was optioned to Triple-A Gwinnet. … Veteran C Jonathan Lucroy has been signed to a minor league contract. The move comes one day after C Tyler Flowers announced his retirement.
BREWERS ROSTER MOVES
The Brewers selected Milner from Triple-A Nashville and optioned LHP Eric Lauer there.
Braves: RHP Huascar Ynoa (4-1, 2.23 ERA) makes his eighth start of the season.
Brewers: RHP Freddy Peralta (3-1, 2.77 ERA) makes his eighth start of the season.