Narveson (7-6) yielded a two-run homer to Aramis Ramirez in the first, but then settled down to hold the Cubs scoreless on eight hits over five innings, walking one and fanning three.
Kameron Loe, LaTroy Hawkins and Francisco Rodriguez each hurled a scoreless relief inning and John Axford pitched a 1-2-3 ninth for the Brewers, who remained one-half game out of first place in the National League Central.
Milwaukee erased the 2-0 deficit in the bottom of the first on Ryan Braun's run-scoring double and a two-run triple by Casey McGehee.
Ryan Dempster (7-8) surrendered three runs on seven hits in a six-inning start for the Cubs, who dropped the first of a three-game set.
Celebrity Families of 2014 [PHOTOS]