Jonathan Lucroy accounted for Milwaukee's other two runs with a solo shot and an RBI single.
Chris Narveson (1-0) went five innings for the win, allowing three runs -- two earned -- on six hits and struck out four. Francisco Rodriguez picked up the save by retiring the final two batters in the ninth.
Naverson took the mound at chilly Wrigley Field with a 5-0 lead that was capped when Gonzalez got a hold of a cut fastball from Cubs starter Paul Maholm (0-1) and launched it into the left field seats.
Maholm struggled with his control in his Chicago debut. The former Pirate allowed six runs on six hits in four innings.
Alfonso Soriano had two RBI for the Cubs, who fell to 1-4 for the young season.
2014: The Year in Music [PHOTOS]