Jean-Gabriel Pageau scored twice, Casey Cizikas had a goal and an assist, and Ilya Sorokin made 24 saves for the Islanders (22-15-2), who bounced back from 4-1 loss at the Seattle Kraken on Sunday for their fourth win in five games.
"A good team learns from its mistakes," Pageau said. "[Sorokin] was outstanding, kept us in it, and we answered. Every line and all three pairings of 'D' played amazing after that. That was a great team effort. Great win. Big win for us."
Bo Horvat scored twice, and Spencer Martin made 23 saves for the Canucks (16-18-3), who have lost three in a row.
"We kind of did this one to ourselves if I'm being honest," Horvat said. "Every turnover resulted in a goal, and I think that was the story of the game for us."
Horvat put the Canucks ahead 1-0 at 18:23 of the first period on a redirection of Oliver Ekman-Larsson's point shot.
After the first period, during which the Islanders were outshot 12-10, New York coach Lane Lambert decided to switch up his lines.
"More grabbing attention," Lambert said. "I felt like we could play better, and so did they."
Aatu Raty tied it 1-1 at 2:36 of the second. The 20-year-old rookie, who was playing his fifth NHL game, received a pass from Ross Johnston on a 2-on-1 and waited for Martin to slide over before shooting back across the grain for his second goal.