Zambrano struck out four of the first six batters he faced and cruised through three perfect innings to start the game at Milwaukee.
He then allowed a solo home run to Rickie Weeks to lead off the fourth.
Chicago's Ryan Dempster pitched the ninth for his second save.
Brewers starter Ben Sheets gave up five runs and nine hits in six innings to take the loss.
Sheets gave up two runs in the second inning, allowing an R-B-I triple by Mark DeRosa and a two-out R-B-I single by Zambrano.
Sheets breezed through three scoreless innings before struggling in the sixth. Derrek Lee led off with an infield hit, and Aramis Ramirez clobbered a two-run homer to left center field to put Chicago ahead 4-to-1.