Ryan Callahan and Derek Stepan also scored for New York, which won a third straight and sixth in seven games.
Henrik Lundqvist turned aside 24-of-25 shots to earn the victory.
Alex Ovechkin notched his NHL-best 35th goal for the struggling Capitals, who absorbed a fifth consecutive defeat -- their longest losing skid since 2010.
Philipp Grubauer started in net but was pulled in the first period after allowing three goals on the Rangers' first eight shots.
Braden Holtby turned aside 17-of-18 tries the rest of the way.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut