The Braves trailed 4-1 heading to the bottom of the sixth.
B.J. Upton hit a two-out homer, barely clearing the right-field wall, and the Braves rallied for the win the next inning. Gerald Laird also had a key hit, a run-scoring double that ricocheted off an infielder's glove.
Jean Segura had three hits for Milwaukee and scored two runs, driven home both times by two-out hits from Jonathan Lucroy.
Alex Wood (4-5) worked a scoreless inning for the win, and Craig Kimbrel earned his 12th save.