Alexandar Georgiev made 42 saves for the Rangers (34-24-4), who have won four straight and are 8-1-0 in their past nine games. The Rangers trail the Columbus Blue Jackets by four points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
The Rangers set a team record with their eighth straight road victory; they had previously won seven in a row twice (Jan. 12-Feb. 12, 1935, and Oct. 28-Nov. 29, 1978).
"I think the whole game, we played pretty smart," Zibanejad said. "Obviously, we don't want to lose a 3-1 lead and give them a point like that, but we'll take the two and keep going."
Varlamov made 24 saves for the Islanders (35-20-7), who moved one point ahead of the Blue Jackets for the first wild card in the East.