Goldschmidt, who has made big hits a habit since being called up from double-A Mobile on Aug. 1, gave Arizona a 7-1 lead in the fifth inning with a two-out home run to right field against Shaun Marcum after Miguel Montero was intentionally walked.
"Obviously, it was exciting, exciting game," Goldschmidt said. "Glad we could get the win right here."
Montero drove in two runs with a single and a double, helping cut Milwaukee's lead to 2-1 in the best-of-five series. Game 4 is Wednesday night in Phoenix.
"It's not a do-or-die game," Milwaukee Manager Ron Roenicke said. "We need to come out and play a solid game, but certainly not do or die."
With an unorthodox overhand style he says comes from throwing tomahawks as a kid in the Michigan woods, Collmenter limited the Brewers to a run and two hits in seven innings.
Corey Hart's leadoff homer in the third inning was the only run Milwaukee has scored against the 25-year-old in 21 innings.
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