Sergei Bobrovsky made 18 saves, and Cam Atkinson hit the goal post twice for Columbus (38-28-3), which remained tied in points with the Montreal Canadiens for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
The Blue Jackets have been shut out in three of their past six games.
"You take out the first eight minutes of the first period, which was frustrating to me how we started, but after that I thought we played really well," Columbus coach John Tortorella said. "I think you have to give their goaltender a little bit of props tonight, making some saves. But I think some of our main chances, we don't get to the net."
Greiss started for the third straight game after Robin Lehner sustained an upper-body injury during a 5-4 shootout win against the Ottawa Senators last Tuesday. Lehner is day to day.
Lehner has played 38 games this season; Monday was Greiss' 37th.
"If everything progresses well, I don't think Robin will be too long," Islanders coach Barry Trotz said. "We've got a couple of days here [until our next game], so the timing couldn't be better.
"We haven't overextended our goalies all year, so I don't see any reason for concern."
Pulock gave the Islanders a 1-0 lead 6:11 into the game on a one-timer from outside the right circle after Cal Clutterbuck's shot from the left point hit Blue Jackets defenseman Markus Nutivaara in front of the net.
It was Pulock's eighth of the season and third straight goal by an Islanders defenseman; Scott Mayfield and Nick Leddy scored in a 5-2 loss against the Philadelphia Flyers on Saturday.
"Nowadays in this League, the D-men have to help out in that aspect," said Pulock, who has an NHL career-high 33 points. "When you can kind of get those goals from the back end, it takes a little weight off the forwards. All we needed was the one tonight, so it was a big goal."
Bobrovsky prevented New York from doubling its lead when he slid to his left to deny Lee's one-timer on a 2-on-1 with Jordan Eberle at 14:08 of the second period.
Greiss kept the Blue Jackets off the scoreboard with back-to-back saves against Josh Anderson and Matt Duchene with 1:30 remaining in the second.
"It's frustrating," Duchene said. "We were the better team tonight, bottom line. I don't even know if they got to 20 [shots]. I think they had 18 shots before that empty-net goal.
"We took over the second half of the game. Three goal posts, and Greiss played well on the other plays. There's a lot of good things to take away from that one. We can't dwell on this one. We've got to get ready for the next one."
Lee scored an empty-net goal at 18:30 of the third.
"It seems like these two points are always worth more than just two," Lee said. "This was a big one tonight. Obviously, we're looking forward to our next one."
