The contest was knotted in a scoreless tie until the ninth, when the Brewers exploded for five runs on four hits to win going away.
Two outs later, Bianchi lined two-bagger to right field, scoring Lucroy and Gomez.
Blake Parker then took the mound and after fanning Yuniesky Betancourt, surrendered another two-run double to Weeks as the Brewers took the opener of a four-game set.
Brandon Kintzler (3-0) got the win in relief of starter Kyle Lohse, who scattered five hits over six shutout innings.
Cubs starter Jeff Samardzija fired seven scoreless frames, allowing three hits while striking out seven.