Zimmerman's two-run shot triggered a big first inning that handed the Nationals a quick 4-0 lead and he added a solo blast in the third for a 5-0 Washington advantage.
Danny Espinoza and Roger Bernadina each provided three hits and a pair of RBI while Michael Morse went 3-for-5 with three runs scored as the National League East-leading Nats took three wins in a four-game series against their divisional rivals.
Ross Detwiler (5-3) surrendered only one earned run on seven hits over seven innings, walking one and striking out three in notching his first victory as a starter since May 3.
Atlanta's Jair Jurrjens (3-4) was roughed up for six runs on nine hits before exiting after 2 1/3 frames.
Freddie Freeman got the only RBI for the second-place Braves, who fell 3 1/2 games behind Washington in the NL East with the loss.