The Rangers' short-handed tally put them ahead 3-1 and was enough to lift them to their third straight victory and seventh in nine contests overall.
Ryan Callahan added a goal and Ryan McDonagh also lit the lamp for the Eastern Conference-leading Rangers, who were playing the Capitals for the first time since last year's first-round playoff series, which New York lost.
Henrik Lundqvist earned the victory with 24 saves, 10 of which came in the third period.
Washington got a goal and an assist from John Carlson, but still fell for the seventh time in 10 games.
Michal Neuvirth made 25 saves in the setback.