Eric Thames hits three-run homer in bottom of ninth inning
Guerra held that lead until Story hit his 21st home run to lead off the fifth inning to tie it.
Christian Yelich also homered for the Brewers, who kept pace with the Chicago Cubs in the National League Central. Milwaukee trails Chicago by a game for first place.
The Brewers trailed 3-2 entering the ninth when Colorado closer Wade Davis (1-5) blew a save for the second day in a row. He got the first out before issuing two walks. He got Jonathan Schoop to pop up for the second out before the Thames hit a 1-1 fastball into the right-field seats.
It was his 15th of the season.
The loss spoiled another solid outing from Colorado starter German Marquez. Marquez tied a season-high nine strikeouts over seven innings to continue an effective stretch of starts. He has averaged 6 2/3 innings pitched over his last six starts and followed a 3-0 July with a strong start to August.
Carlos Gonzalez homered among his two hits and Trevor Story also homered for the Rockies.
The Brewers nearly spoiled a great start by Junior Guerra, who tossed a season-high eight innings. He allowed three runs on five hits, struck out six and became the first Brewers' starter to pitch that deep into a game this season.
Guerra walked Charlie Blackmon to lead off the sixth inning, and Gonzalez launched a 3-2 pitch over the fence in right to give the Rockies a 3-1 lead. It was Gonzalez's 14th home run of the season.
Yelich led off the bottom of the inning with his 17th home run to make it 3-2.
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