Zimmermann, making his third spring start, tossed four perfect innings and struck out four against a Yankees lineup that included Jacoby Ellsbury, Brett Gardner, Mark Teixeira and Brian McCann. The right-hander now has nine scoreless innings to his credit in Grapefruit League play.
"I feel like I'm ready to go," Zimmermann said. "Now it's just building up arm strength and getting up to 80, 90 pitches before the season starts. My stuff is pretty sharp right now."
Sabathia wasn't nearly so sharp in his second outing of the spring. The lefty surrendered three runs on four hits over three innings, walking two and striking out three.
"I was kind of erratic, just all over the place," Sabathia said. "Couldn't really keep my delivery down. And to try to push off and get some leverage throwing downhill was hard for me."
Sabathia walked leadoff man Anthony Rendon in the first and saw him come around to score on a Wilson Ramos fielder's-choice grounder. The lefty also issued a free pass to start the second, putting Danny Espinosa aboard. Later in the inning, Anthony Rendon smoked a two-run double down the left-field line.
Once Zimmermann came out of the game, the Yankees made a little noise offensively. Third baseman Dean Anna singled home Eduardo Nunez in the fifth off Drew Storen to cut the Nats' lead to 3-1. In the sixth, Zoilo Almonte doubled off the wall in left-center against lefty Felipe Rivero, and Gardner drove him home with a sacrifice fly to deep center.
Although Gardner had the sac fly, he combined with Ellsbury, Teixeira and McCann to go 0-for-11 in the game.
Jayson Werth had two hits for Washington after a 1-for-6 start to the spring.
Up next: The Nationals have a pair of split-squad road games on Wednesday, facing the Astros in Kissimmee, Fla., live on MLB.TV, and the Braves in Lake Buena Vista, on Gameday Audio. Both games start at 1:05 p.m. ET. First-year manager Matt Williams will take his staff to Kissimmee, where the Nats will take part in their first game featuring a test of the new instant replay system. Tanner Roark will start that contest, while fellow right-hander Chris Young will take the ball against Atlanta.