The Nationals prevented Atlanta from clinching the National League East title, although the Braves ensured themselves no worse than a tie for the crown earlier in the day when they downed the Chicago Cubs 9-5.
A win by Atlanta or a loss by Washington during the remainder of the season will give the division championship to the Braves.
Zimmermann (19-8) won his fourth straight start, taking a no-hitter into the sixth and throwing his second shutout of the season and of his career.
Washington sent 11 men to the plate in the bottom of the sixth, during which the Nationals scored seven runs on seven hits. Jayson Werth doubled home the first two runs of the inning and a triple by Denard Span brought home the final two.
Jacob Turner (3-8) allowed only two hits through the first five innings, but was charged with five of the seven runs Washington scored in the sixth.
The only hit off Zimmermann was a single by Donovan Solano with two out in the sixth. The Washington starter walked one, struck out nine and threw 109 pitches.