Tyler Thornburg tossed six scoreless innings and Sean Halton hit a grand slam in a five-run first frame as Milwaukee blanked Chicago, 7-0, in the third portion of a four-game series.
Khris Davis added a solo homer and scored twice, with Aramis Ramirez and Carlos Gomez driving in a run each for the Brewers, who have won three straight in the set and four in a row overall.
Thornburg (3-1) allowed only two hits and a pair of walks while striking out four, turning in his second start of the season where he held an opponent scoreless.
"He's pitching great," Brewers manager Ron Roenicke said of Thornburg. "He's confident. He's got three really good pitches."
Chris Rusin (2-5) was tagged for four hits and six runs over four full frames for the Cubs, losers of five straight and seven of eight.
"He's just kind of missing with his curveball," Cubs manager Dale Sveum said of Rusin. "His curveball was real close but it just kept missing, but you know he battled."
The Brewers provided Thornburg with a bushel of support, right off the bat. Jean Segura walked with one down and moved up on a Jonathan Lucroy single before crossing home on a Ramirez base hit. Khris Davis walked two batters later to load the bases and Halton launched his first career grand slam to right which capped the burst.
Davis started the home fourth with his 10th home run of the season to make it 6-0 for the hosts, and Gomez doubled home Norichika Aoki with two away in the fifth for a seven-run spread.
Thornburg retired seven of the last eight batters he faced, then gave way to Jimmy Nelson for the seventh. Nelson stranded two runners by inducing a groundout from pinch-hitter Junior Lake in that frame, then fanned two in the eighth.
Michael Blazek worked around a Nate Schierholtz leadoff single in the ninth, setting down the next three batters to cap the victory.