Hendricks struck out five and walked one in his third consecutive win, continuing an impressive opening run for his major league career. The right-hander is 4-1 with a 1.01 ERA in five starts since he got a no-decision in his debut at Cincinnati on July 10.
Anthony Rizzo hit his 26th homer for Chicago, which had lost three of four. Arismendy Alcantara had two hits and drove in a run after going 1 for 14 through the first four games of the Cubs' seven-game homestand.
Trying for a major league-high 15th win, Peralta allowed three runs and seven hits in 6 1-3 innings. The right-hander had won each of his last five starts and was 10-1 with a 4.06 ERA in his previous 12 games coming into the night.
Peralta (14-7) has lost each of his three starts this season against last-place Chicago. He is 6-0 with a 1.10 ERA in seven games against the rest of the NL Central.
The Cubs grabbed the lead on Justin Ruggiano's RBI single in the second, and Alcantara added another run-scoring single in the fourth. Alcantara's hit drove in Starlin Castro, who reached on a leadoff double to extend his hitting streak to 11 games, the best such streak for the Cubs this year.
Rizzo then led off the sixth with a towering drive to left for his first homer since July 22.
Pedro Strop replaced Hendricks (4-1) with the bases loaded in the eighth and got Jonathan Lucroy to ground into an inning-ending double play. Hector Rondon then got three outs for his 15th save in 19 chances.
NL Central-leading Milwaukee had won four of five.
Brewers center fielder Carlos Gomez made a great leaping grab on the warning track in the first, taking extra bases away from Javier Baez. Gomez then was hit by a pitch on his right wrist in the third, but stayed in the game.
Brewers: INFs Jean Segura and Scooter Gennett are playing with quad injuries. Manager Ron Roenicke said Segura is doing a lot better, but Gennett "is still a little bit limited."
Cubs: LHP Felix Doubront (strained left calf) struck out seven while pitching four-plus innings in his first rehab appearance with Triple-A Iowa. He was charged with three runs and four hits.
Brewers RHP Kyle Lohse (11-6, 3.33 ERA) and Cubs LHP Tsuyoshi Wada (1-1, 3.25 ERA) are slated to start the third game of the series Wednesday night. Lohse is 2-0 with a 1.69 ERA in two starts against Chicago this season, including a three-hitter in a 9-0 victory on June 1. Wada is making his first appearance against Milwaukee and his sixth career start overall.
Jay Cohen can be reached at http://www.twitter.com/jcohenap
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