Maldonado's two-bagger highlighted a four-run first inning that ignited a 12-hit attack and carried the Brewers to a decisive win in the first of a three-game series at Miller Park.
Ryan Braun added three hits, including an RBI double, while Norichika Aoki went 3-for-4 with a run scored for Milwaukee.
Marco Estrada (1-0) limited the Cubs to two runs on five hits over seven innings, striking out six while walking one.
Jim Henderson recorded his first save after Brandon Kintzler had allowed two Chicago runs in the ninth.
Cubs starter Edwin Jackson (0-1) gave up five runs on eight hits in six frames.
Welington Castillo bashed a two-run homer for Chicago.