MILWAUKEE — Ian Happ hit a three-run homer, newly acquired left-hander David Peterson bounced back for the win after giving up a home run on his first pitch as a Cub, and Chicago beat the Milwaukee Brewers 8-2 on Saturday night.

Happ’s 17th homer capped a four-run sixth that put the Cubs up 6-2.

Peterson (4-6), acquired Thursday from the Mets to bolster an injury-riddled rotation, allowed Jackson Chourio’s 11th homer on his first pitch, but then settled in to allow two runs on five hits in 5 2/3 innings.

Seiya Suzuki and Michael Conforto also homered for the Cubs, who moved 6 1/2 games behind the NL Central-leading Brewers, who had won the first four meetings between the teams this season.

Chad Patrick (5-4) relieved to open the sixth and retired the first two hitters before issuing a pair of walks. Nico Hoerner followed with an RBI single to put the Cubs up 3-2. Happ then sent the first pitch 381 feet to right for his first homer since June 13.

Alex Bregman’s sacrifice fly in the seventh increased the lead to 7-2. Conforto added a pinch-hit homer in the ninth.

Kyle Harrison retired the first 10 hitters before Matt Shaw singled up the middle with one out in the fourth. Suzuki followed with his 12th homer to put Chicago up 2-1.

The Brewers tied it 2-all in the fifth when Blake Perkins doubled to open and Sal Frelick followed with an RBI single.

The Cubs acquired Peterson in exchange for minor-league infielder Cole Mathis after starters Edward Cabrera and Ben Brown joined three other starters on the injured list.