Chacin (6-1) allowed four hits in six innings, striking out seven and walking four to win his sixth consecutive decision. Jeremy Jeffress pitched the seventh, Josh Hader struck out the side in the eighth and Cory Knebel finished with a perfect ninth for his sixth save.
Mike Montgomery (2-2) allowed only two hits in six innings, both by Cain. He struck out four and walked one in his fourth start since replacing injured Yu Darvish in the rotation.
Cain drove a 3-1 pitch over the wall in left with one out in the third for his eighth homer. He also opened the first inning with a single.
The Brewers improved to 3-8 this season against the Cubs and moved 1 1/2 games ahead of second-place Chicago in the N.L. Central.
The Cubs won Monday’s series opener 7-2 with five runs in the 11th, but managed just two hits in Tuesday’s 4-0 loss.
The Brewers stranded runners at third in each of the first two innings. In the second, rightfielder Jason Heyward prevented a run, charging in for a sensational sliding grab on Erik Kratz’s one-out sinking liner and then recovering quickly to hold Hernan Perez at third.
Cubs: RHP Yu Darvish, on the 10-day DL (right triceps tendinitis) and RHP Carl Edwards, also on the DL (right shoulder inflammation), each came through Tuesday’s bullpen session well, manager Joe Maddon said.
Brewers: RHP Matt Albers, on the 10-day DL (right shoulder discomfort), will continue treatment throughout the weekend, and then be reassessed. . RHP Zach Davies, on the 10-day DL retroactive to May 30 (right rotator cuff inflammation), threw a bullpen session Wednesday, but is at least three weeks away and will need two or three rehab outings, manager Craig Counsell said.
Cubs: Chicago is off Thursday, then heads to St. Louis for a three-game series against the Cardinals. Left-hander Jon Lester (7-2, 2.22) starts for the Cubs, opposed by Michael Wacha (8-1, 2.47). Lester has won his last three starts, and is 6-2 with a 1.72 ERA in his last 10.
Brewers: After a day off, Milwaukee opens a three-game home series against the Phillies on Friday. Brent Suter (6-4, 4.61) starts the opener. The left-hander has yet to record a quality start in 12 tries, with his longest outing 5 2/3 innings.
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Source: Fox Sports