Simon Holmstrom made it 2-0 at 18:29 when he roofed a wrist shot after a pass from behind the net by Pageau.
Zach Parise gave New York a 3-0 lead at 3:38 of the second on a redirection of Pageau's shot from the edge of the right circle, and Horvat swatted a feed from Barzal in the right circle at 5:08 to make it 4-0.
"I didn't give him a great pass," Barzal said. "I gave him kind of a bad puck and he buried it. It's almost a relieving feeling. He's a goal-scorer, right? So, he can hit those and just has a really good knack for goal-scoring."
Immediately after his goal, the crowd of 17,255 began chanting Horvat's name.
"It was pretty amazing," Horvat said. "I haven't had a chant like that in a building that loud I don't think ever, so that was pretty amazing."
Sorokin made 13 saves in the second and 11 in the third period.
"Our goaltender played well for us and gave us an opportunity to get our legs under us," Islanders coach Lane Lambert said.
NOTES:Horvat will face his former team Thursday when New York hosts Vancouver. … It was Sorokin's 15th NHL shutout in 110 starts. … Bolduc replaced defenseman Alexander Romanov, who did not play because of personal reasons. Lambert said he does not expect Romanov to be out for an extended period. … It was the first time the Islanders scored four goals in a game since Jan. 3 (16 games). … New York center Brock Nelson extended his point streak to eight games (four goals, five assists). … Islanders defenseman Scott Mayfield got his 100th NHL point with an assist on Bolduc's goal. Mayfield and Islanders defenseman Ryan Pulock each played his 400th NHL game. … Seattle forward Eeli Tolvanen was minus-3 in 17:38 of ice time.