Estrada (7-4) allowed only two hits and three walks in the 115-pitch performance, striking out six.
Aramis Ramirez went 3-for-4 with solo shot while Jonathan Lucroy added a two-run blast and Carlos Gomez also went deep with the bases empty for Milwaukee, which took the opener of a three-game series.
Mike Minor (13-8) was tagged with the loss, surrendering three runs on eight hits over seven innings for the National League East champion Braves.
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