Matias Maccelli had a goal and an assist, and Matthew Schaefer had two assists for the Islanders (3-3-0). Ilya Sorokin made 23 saves.
Brock Boeser and Max Sasson scored for the Canucks (2-6-0), who have lost five straight. Leevi Merilainen made 35 saves.
Palmieri gave the Islanders a 1-0 lead at 14:57 of the first period. With his back to the goal, he deflected Matthew Kessel's shot from the right point over the blocker of Merilainen.
Maccelli doubled the Islanders’ lead just 53 seconds later. He beat Merilainen high to the blocker side from the left circle off a feed from Schaefer, who had intercepted a clearing attempt from Zeev Buium.
Sasson cut the deficit to 2-1 at 7:52 of the second period. He skated into a loose puck in the left circle and beat Sorokin under his glove.
Boeser tied the game 2-2 while on a power play at 18:55, scoring blocker side with a one-timer from the top edge of the right circle off a pass from Elias Pettersson.
Sorokin kept the game tied by sliding over twice to stop multiple one-timers from Linus Karlsson. His first save came at 1:53 of the third period before he denied the forward again at 2:05 while Vancouver was on a power play.
Palmieri scored his second of the game at 5:38 to give the Islanders a 3-2 lead. Maccelli, who was below the goal line, fed Palmieri in the slot for a wrist shot that beat Merilainen glove side through a screen.
