Zimmerman (8-6) stretched his unbeaten streak to seven starts, stifling the Brewers on one run over six innings. The right-hander allowed five hits, walked one and struck out six while lowering his ERA to 2.28.
Drew Storen and Sean Burnett each contributed a scoreless relief frame and Tyler Clippard followed suit, striking out a pair in the ninth for his 19th save as National League East-leading Washington took a 2-1 lead in the four-game series.
Corey Brown socked a solo homer and Tyler Moore added a two-run shot in the fourth inning for the Nationals.
Milwaukee's Randy Wolf (3-7) was tagged for four runs on nine hits in over seven full innings.
Rickie Weeks provided the Brewers' only RBI.