Gindl tripled home Scooter Gennett and then scored on Martin Maldonado's sacrifice fly in the fourth inning, handing the Brewers a 2-0 lead.
The Milwaukee left-fielder later capped the scoring with a two-run shot in the seventh as the Brewers breezed in the opener of a four-game series.
Wily Peralta (10-15) yielded just one unearned run on five hits over six innings to notch the decision. He walked two and struck out seven.
Cubs starter Edwin Jackson (8-16) allowed two runs on two hits and three walks in a four-inning performance.
Starlin Castro drove in Chicago's only run.
Celebrity Families of 2014 [PHOTOS]