Chacin (6-1) permitted four hits and walked three while striking out seven in winning his sixth consecutive decision since an April 4 loss to St. Louis. The outing also capped a dominant series for Brewers starters as Junior Guerra, Chase Anderson and Chacin teamed to allow just one run in 19 innings, fanning 17.
Jeremy Jeffress, Josh Hader and Corey Knebel took care of the rest. Jeffress tossed a scoreless seventh and Hader worked the eighth, striking out the side to give him 75 whiffs in 38 innings this year.
Knebel earned the last three outs for his sixth save in eight chances.
Mike Montgomery (2-2) was saddled with the loss despite an excellent outing. Montgomery ceded just two hits and a run over six innings, walking one and punching out four.
One of the two hits, though, left the park. Cain turned on an inside fastball with one out in the third, pulling it 374 feet over the wall in left for his eighth homer of the year.
Chacin artfully worked out of a spate of jams, including one in the fourth. Kyle Schwarber and Javier Baez singled with two outs and Chris Gimenez came close to cashing them in when he clouted a hanging breaking ball deep to left. But Ryan Braun ran it down on the warning track.
An inning later, consecutive one-out walks to Ben Zobrist and Jason Heyward set the table. But Chacin fanned Tommy La Stella and retired Anthony Rizzo on a grounder to first baseman Jesus Aguilar.
Chicago's last baserunner came on a two-out single in the eighth by Ian Happ. But Hader reared back and blew a full-count fastball by Schwarber to end the inning.
In taking a 1 1/2-game lead in the National League Central, the Brewers recorded their first back-to-back shutouts of the Cubs since 2006.
--Field Level Media