Cal Clutterbuck almost scored for New York while shorthanded 31 seconds into the third period, but he shot off the crossbar after taking a backhand pass from Jean-Gabriel Pageau on a 2-on-1.
"I think the second goal really took a lot out of us," Islanders coach Barry Trotz said. "And then we come out and we hit the crossbar shorthanded to start the third, and it was sort of like our night, just the way everything was going. Instead of getting a lot of momentum off that 5-on-3 (penalty kill), we had a defenseman jump by us and it bounces off the back wall and makes it a greasy goal.
"We didn't have enough push. They backed it up pretty good. They did a good job of keeping everybody back. So we can be better. We can be better. Our game wasn't a 4-1 game, in my opinion."
Zucker pushed the lead to 3-0 at 9:11 of the third with a one-timer from the top of the crease after receiving a pass Rust sent from behind the net.
"When they have to start chasing, they have to come out of their system," Zucker said. "We can have a little bit more freedom to play the game and play smart, but keep attacking."
Nelson cut it to 3-1 by tipping in a centering pass from Bailey on a power play at 15:39 before Rust scored an empty-net goal for the 4-1 final at 16:54.
"We've had a good run," Nelson said. "Trying to bank as many points as you can with the shortened season and only playing in our division. Tonight was a tough one. ... Just weren't able to get one, get some momentum and kind of feed off that. Then we found ourselves in a hole."