Braun finished 4-for-6 with five RBI -- including his three-run shot in the final frame -- giving him National League-leading 35 for the season, while Ramirez also went deep in the fifth for the Brewers, ending with four RBI.
Carlos Gomez went 4-for-5 with a solo shot as Milwaukee banged out 21 hits, including eight in the last inning when the Brewers sent 14 men to the plate.
Marco Estrada (2-5) earned the win, yielding three unearned runs on six hits over five frames as the Brewers romped in the opener of a four-game series.
Cubs starter Justin Germano (2-4) was tagged for five runs on 10 hits over five full innings.
Chicago sent outfielder Joe Mather to the mound in the ninth to mop up in the big loss.
Brett Jackson socked a solo homer for the Cubs.