With two outs in the eighth, Bud Norris (1-6) walked Jonathan Villar, who stole second base. Gennett then lined a single to right field. Villar scored as Nick Markakis' throw to the plate from right field was up the third-base line.
Ryan Braun's eighth homer gave the Brewers a 1-0 lead in the fourth.
Atlanta's Julio Teheran set a personal high with 12 strikeouts while allowing one run in seven innings.
Jimmy Nelson allowed one run in six innings for Milwaukee.
Snitker, the former Triple-A Gwinnett manager, was promoted after Fredi Gonzalez was fired on May 17.
Michael Blazek (2-1) pitched a scoreless seventh. Jeremy Jeffress recorded the final three outs to earn his 12th save.
