Pulock, who went 41 games this season without a goal, took a cross-ice feed from Mathew Barzal and scored with a wrist shot from the right circle.
"Throughout my career, I've been able to score a little bit and to kind of go through a little slump like that, it's tough," Pulock said. "As the games went on it got tougher, but I knew I just needed to get that one. Obviously it came in a big moment, and I'm excited about that."
Kyle Palmieri scored his first goal with the Islanders (27-11-4), who salvaged a split of a two-game set and went 5-1-0 on their six-game homestand. Ilya Sorokin made 24 saves.
It was Pulock's first regular-season goal since March 7, 2020.
"He was squeezing it," Islanders coach Barry Trotz said. "He was trying to put the puck through the end boards he was trying so hard. I think this will just get him to relax a little bit. … It was really nice to see."
Libor Hajek and Brendan Smith scored for the Rangers (19-16-6), who have gotten at least one point in six of seven. Igor Shesterkin made 29 saves.
"I thought we did a lot of good things," Smith said. "At this time, points are good. We want two, but we're trying to get back into the hunt and get into that playoff spot, so we'll take the points."