Braun contributed an RBI single during the Brewers' three-run first inning and socked a bases empty-homer in the fifth to give Milwaukee a 5-2 lead off Astros starter Lucas Harrell (1-1).
Milwaukee ended up needing that run when Jose Veras surrendered three Houston runs in the seventh.
Zack Greinke (2-1) earned the victory, yielding two runs on eight hits over six innings.
John Axford nailed down his third save in the ninth as Milwaukee took the first of three-game series.
Harrell was lit up for five runs on five hits in a five-inning start.
Brian Bogusevic drove in three with a two-run triple and a bases-loaded walk for the Astros.
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