Hischier scored, and Allen made 11 saves for the Devils (28-27-2), who have lost five of their past six games.
"One play cost us the game," said Hischier, who will represent Team Switzerland in the Olympics. "We did a lot of good things but at the end, come up short again. We should have just tried to get that overtime and try to get the second point there. It [stinks] to have that as our last game but the break is there to flush everything and hopefully we come back and everybody has a fresh mindset and re-attack."
Casey Cizikas gave the Islanders a 1-0 lead, knocking in a rebound from the slot at 6:30 of the second period.
"There was nothing out there tonight," Islanders captain Anders Lee said. "I thought this was the best defensive game [the Devils] played. They were on our backs coming out of our zone. In the neutral zone, they were there on our backs, and then even in the offensive zone. It was tough to get free tonight, really tough, but we put ourselves in a position for Bo to go win it for us."
Hischier pulled the Devils into a 1-1 tie on a snap shot from the right hashmarks at 18:26. It was New Jersey's first goal in two games after a 3-0 loss to the Columbus Blue Jackets on Tuesday.
"We need to have a certain standard of the way we approach the day, regardless of our situation," Allen said. "Obviously, we understand that over these next three weeks, we'll have a lot of time to reflect on a lot of different things. We’ve got to go on a [heck] of a run; that's what it comes down to.
"We’ve got the guys to do it. It's just a little bit of belief and a little bit of recovery and hopefully some guys come back from the Olympics with some medals and keep going."
Sorokin made 12 saves in the second, stopping a snap shot from low in the right face-off circle by Dougie Hamilton at 13:12, and an uncontested wrist shot by Jesper Bratt from the slot at 14:24.
"It's a huge win not only standings wise, but confidence ... the confidence going into the break," Horvat said. "Knowing we're in a good spot, it's up to us to keep ourselves there and keep getting wins after the break too."
NOTES: The Islanders swept the New York Rangers and Devils in the same season for the first time in franchise history. ... Forward Nick Bjugstad, acquired in trade with the St. Louis Blues on Wednesday, had one shot and three hits in 10:42 of ice time in his Devils debut.