Atlanta's Bobby Cox passed Sparky Anderson when he got his 2,200th win, moving him into sole possession of fourth place on Major League Baseball's all-time managerial victory list.
Kelly Johnson singled in the other run for the Braves, who snapped a three- game losing streak.
Left-hander Chuck James (5-4) allowed one run on five hits, with two walks and eight strikeouts over six innings.
Bob Wickman pitched a perfect ninth for his eighth save of the season.
Prince Fielder homered for the Brewers' lone run.
Starter Chris Capuano (5-4) gave up two runs on seven hits, with two walks and six strikeouts over seven innings for the Brewers, who have lost six straight games.
2014: The Year in Music [PHOTOS]