Marco Estrada tossed seven scoreless innings and Jonathan Lucroy hit a two-run homer as Milwaukee downed Atlanta, 5-0, in the opener of a three-game series.
Estrada (7-4) let up just two hits and three walks while fanning six, with Rob Wooten and Michael Blazek capping the three-hit shutout with a combined two sterling relief frames.
Aramis Ramirez finished with three hits, including a solo homer, and Carlos Gomez also went deep for the Brewers, who have won two in a row since losing three straight.
"It's nice to get a W," said Ramirez. "We haven't played good up until this month so it's good to finish strong."
Mike Minor (13-8) surrendered eight hits and three runs while fanning six over seven full frames for the Braves, who have dropped two of three but still hold a half-game lead over St. Louis for the best record in the National League.
"Yeah, 100 percent, we need to take care of that," Braves outfielder Jordan Schafer said about securing home-field advantage. "That's first and foremost because obviously we've been a pretty good home team"
Gomez launched his 22nd homer of the year to put the Brewers on the board in the first.
Andrelton Simmons tripled in the home second but was stranded there, and Atlanta failed to score in the fourth despite back-to-back walks to open the frame.
It came back to haunt the hosts when Norichika Aoki doubled with one out in the fifth and Lucroy barely reached the seats in right for a 3-0 game.
Ramirez made it 4-0 with one down in the eighth, then Sean Halton kept the inning alive with a double and scored when Yuniesky Betancourt singled and Simmons' throw home bounced off the mound and to the backstop.
Milwaukee has taken three of four from Atlanta this season ... Braves manager Fredi Gonzalez was ejected in the bottom of the seventh inning for arguing that Paul Janish should have been awarded first after being hit on the left thigh. Home plate umpire Angel Hernandez ruled Janish didn't do enough to avoid the pitch.