The 2-1 win was the third in a row for Milwaukee over Chicago. The two teams will wrap up their four game series on Thursday afternoon.
Gallardo, who had a rough outing on opening day against the Cardinals, bounced back, allowing just 5 hits and 1 earned run in his seven innings of work.
Brewers manager Ron Roenicke gave starters Ryan Braun, Corey Hart, and Jonathan Lucroy the afternoon off. Kottaras received the start behind the plate in place of Lucroy, and produced Milwaukee's only two runs with his homer off Cubs starter Ryan Dempster in the top of the 7th inning.
Francisco Rodriguez and John Axford each struck out the side in the 8th and 9th to secure the victory.
Zack Greinke takes the mound for Milwaukee tomorrow afternoon. Matt Garza will start for the Cubs.