The Diamondbacks tied the game in the top of the ninth on Willie Bloomquist's RBI bunt single off of John Axford. They were attempting to become just the eighth team in major league history and first since the 2003 Red Sox to win a best-of-five series after trailing 0-2.
Axford (1-0) suffered his first blown save since April 18, but tossed a scoreless top of the 10th to earn the win.
Jerry Hairston Jr. and Yuniesky Betancourt both had an RBI for the Brewers, who advanced to their first League Championship Series since 1982, when they defeated the Angels in the ALCS before falling to St. Louis in the World Series.
They will open the NLCS Sunday against either the Phillies or Cardinals, who play Game 5 of their NLDS series Friday.