It was the second straight game Washington pitching had limited the Reds to one hit, the first time since 1900 Cincinnati has suffered such a fate.
Zimmerman (4-1) retired the side in order during the first two innings, then surrendered a single to Xavier Paul leading off the third. The Reds put two other men on base, Todd Frazier reaching on a fielding error in the fifth and Corky Miller drawing a walk in the eighth.
The Washington run came in the fourth when Bryce Harper delivered a one-out triple and came on in a single by Jayson Werth. Harper had tried and failed to put down a bunt early in his at-bat.
Homer Bailey (1-2) went seven innings to take the hard-luck loss. He gave up five hits and struck out six.