Semyon Varlamov made 26 saves, including 14 in the third period. He is 3-0-1 in his past four starts.
"He was solid from the start to the end, quite honestly," Roy said. "The save he made at the beginning of the game was a big one for us, and then even in the second he didn't get that many shots, but three good chances and he made some really good saves.
He was solid in front of our net. So, that's the performance that we needed, and it was good for the confidence of our guys."
Ryan Pulock appeared to give New York a 1-0 lead at 7:49 of the first period, but Florida challenged the play for goaltender interference, and the call was reversed after a video review.
Vladimir Tarasenko then scored 24 seconds later to give the Panthers a 1-0 lead. His backdoor pass for Barkov redirected in off the stick of Pageau.
Pulock did tie it 1-1 13:20 of the first, scoring off the post from the right circle after receiving a backhand pass from Pageau from along the end boards.
Barkov gave the Panthers a 2-1 lead at 6:32 of the second period, tapping in a backdoor pass from Sam Reinhart.
Mathew Barzal tied it 2-2 at 8:43 when he redirected in a shot from Noah Dobson.
“That was huge. That is a good team over there,” Barzal said. “I think we did a lot of good things, played very well defensively. ... They had a push. We knew they were going to have a push. I thought we weathered it well.”
Pageau put the Islanders in front 3-2 at 10:42 of the second, getting to a loose puck at the left side of the net and scoring under the arm of a sprawling Anthony Stolarz, who made 21 saves.
The Panthers again challenged the play for goaltender interference, but the call stood after a video review.
“It is never easy in this League," Florida defenseman Aaron Ekblad said. “[The Islanders] are fighting for their lives over there, and they got the better of us."
NOTES: Ekblad returned after missing seven games with a lower-body injury. He was minus-1 in 22:13. ... Barzal's goal was his 23rd of the season, an NHL career high. ... Barkov's goal was his 700th NHL point (262 goals, 438 assists in 728 games). Among Finland-born players in NHL history, only Jari Kurri (483 games), Teemu Selanne (541) and Tomas Sandstrom (719) reached the mark in fewer games.