Rizzo went deep in the third, driving a 3-1 pitch over the wall in center for his 15th homer — matching his career high set a year ago. Castro connected an inning later, making it 3-0 with a drive to the bleachers in left.
"It's an ever-going process," said Rizzo, who went 6 for 14 in the series. "You just got to show up every day and prepare, do your best and play hard. Really grind the at-bats and try to take good swings and just go from there."
The six runs were more than enough for Jackson (7-11), who allowed eight hits in his longest outing of the season. The right-hander finished July with a 3-1 record and a 1.83 ERA in five starts.
"When his command's on, he's going to throw a good game," Brewers manager Ron Roenicke said. "He had good command today. I think the last four or five games, he's thrown the ball really well. "
The Brewers got a runner to third in the third, fourth and fifth innings and failed to score each time. Lucroy was thrown out at the plate by left fielder Julio Borbon when he tried to score from second on Gindl's base hit in the fourth.
Chicago and Milwaukee, the two worst teams in the NL Central, did not make a trade on a quiet deadline day throughout baseball. The Cubs and Cardinals talked about veteran catcher Dioner Navarro, but he was still in Chicago at the end of the night.
"I think one thing is obvious from today, if you look around the league, is that people hold real tight to their young players," Cubs general manager Jed Hoyer said. "We need to get a lot more of them. That part isn't going to change."
There wasn't much left for Hoyer to trade by the end of the month. The Cubs made three major deals in July, trading away pitchers Scott Feldman and Matt Garza, and slugger Alfonso Soriano. They received an array of prospects in return, strengthening their burgeoning minor league system.