Chicago won two of three in Milwaukee, the first time the Cubs had won a series on the Brewers' home field since September 2010.
The Cubs scored all their runs in the second, third and fourth innings to take a 7-0 lead, making things easy for starter Matt Garza.
Garza (3-1) went seven innings, giving up a run on eight hits. He also went 2-for-3 at the plate and scored a run in the fourth on a sacrifice fly.
Wily Peralta (5-9) took the loss, allowing all of the Chicago runs while pitching five innings.
The four Chicago runs in the third were unearned thanks to two Milwaukee errors. Without those errors, the inning would have been over before Navarro came to the plate. He drilled his seventh home run of the season to bring home Ryan Sweeney and Brian Bogusevic.