Burnitz, who turns 36 Friday, would later add some insurance in the sixth inning, courtesy of his first home run in a Cubs uniform. He launched a 1-0 pitch from Brewers starter Ben Sheets out to center field that extended the Cubs' lead to 2-0.
Another single from Zambrano in the seventh, followed by one from Corey Patterson, set the stage for a two-run double to deep right by Todd Walker thus bringing the score to 4-0. Zambrano left the game with one away in the eighth after walking catcher Chad Moeller. (Last season at Coors Field in Colorado, Zambrano threw a complete game, two-hit shutout.)
Chad Fox then came on in relief and got J.J. Hardy to bounce into an inning-ending double play, and one day after blowing his first save of the season, LaTroy Hawkins worked a perfect ninth inning in relief.
Sheets (1-1) went seven innings, giving up all four runs on eight hits. He managed five strikeouts and two walks.
The series finale is set for 1:20 p.m. (CDT) Sunday with Greg Maddux (0-1, 9.00) facing Victor Santos (NR).