WATCH: [All Islanders vs. Devils highlights]
"I know [Vatanen's] a shooter and he does a really good job of keeping his head up and making sure he can get them through," Palmieri said. "It was a good forecheck shift by our line and the puck popped out to him and I just tried to get to the net front. Luckily enough I got rewarded."
Taylor Hall had two assists, and Keith Kinkaid made 30 saves for the Devils (32-22-8, 72 points), who lead the Columbus Blue Jackets by five points for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
"It was huge win. The guys did a good job, didn't give up much, and at the end, we're [blocking] pucks," Kinkaid said. "That's playoff hockey right there. Credit to our guys who sacrificed their bodies and when it did go through, I did my best to make a big save."
Hall extended his point streak to 14 games (nine goals, nine assists), the longest in the NHL. He has 30 points (14 goals, 16 assists) in a personal 21-game point streak; he missed three games with a thumb injury (Jan. 22-25).
Jordan Eberle scored, and Halak made 31 saves for the Islanders (29-27-7, 65 points), who have lost three straight (0-2-1) and are two points behind the Blue Jackets for the second wild card into the playoffs from the Eastern Conference.
"Especially (because) it's a third period comeback, it's deflating," Eberle said. "We had a real opportunity here to start moving up and you give up a game like that, it knocks you back a little bit. It's frustrating. We've got to find a way to pick ourselves up here and you've just got to keep going."
Eberle gave the Islanders a 1-0 lead when he tipped in a pass from Anthony Beauvillier at the right post at 3:55 of the second period. Mathew Barzal got an assist on the goal and leads all rookies in assists (49) and points (66).
The Devils retired the No. 26 jersey of Patrik Elias in a ceremony prior to the game.
"From the start of that ceremony, it gave you some chills when they announced Patty's name and he came down from the stands," Palmieri said. "It was a cool event and a little different because you don't do that very often; it's nice to get him a win."