Zimmermann (5-1) gave up two hits and struck out eight without walking a batter. He threw a one-hit, complete-game against Cincinnati in his previous start.
Rafael Soriano completed the shutout against the Braves by working a perfect ninth for his eighth save.
The Washington scoring came on a two-run homer from Ian Desmond in the fourth after Bryce Harper had drawn a leadoff walk.
Those runs were scored against Paul Maholm (3-3), who allowed just three hits over eight innings.
Atlanta's hits came on a two-out single in the first inning by Justin Upton and a one-out double from Paul Maholm in the third.
After Maholm reached base, Zimmermann retired 17 batters in a row.