Jeremy Hazelbaker's third homer of the season extended the Cardinals' lead to 7-0 in the seventh.
The rookie's shot to right field off a 1-0 slider from Brewers reliever Chris Capuano traveled 406 feet and scored Matt Carpenter, who doubled to start the inning.
Hazelbaker, who has now had 26 at-bats this season, is two-for-four today with the homer and an infield single. He now leads the club in home runs.
Cardinals starter Jaime Garcia is firing along with his offense. He set a new career-high with 11 strikeouts. Garcia has surrendered one hit and one walk though eight scoreless innings.