The Islanders took a 1-0 lead at 4:51 of the second period. Pageau received a feed from Alexander Romanov and scored from the left face-off circle with a one-timer over the glove of Kuemper.
"To be honest, I shot it as hard as I could," Pageau said. "Bounces were kind of on my side today. Some nights, most of them, the bounces haven't [been on my side] so far, but if you keep digging and keep grinding, sometimes it goes your way, and it felt good."
Noah Dobson extended it to 2-0 at 6:01. He skated onto a Mathew Barzal drop pass at the top of the right circle and scored with a slap shot to the glove side.
Gauthier scored twice within 18 seconds to make it 4-0 in the third period.
He put home a rebound from the slot at 10:10 following a Pageau wrist shot, then finished with a backhand around the right pad of Kuemper at 10:28 off a pass from Pageau.
"It feels awesome," Gauthier said of his first multigoal game in the NHL (169 games). "It was fun to see our line get going like that. I thought we got rewarded, because a lot of games we were playing really well, but it just wasn't really going in. So it was fun tonight to also see Jean-Gabriel Pageau getting all those points. I was really happy for him."