In Uniondale, N.Y., Mike Bossy's goal late in the third period gave New York the tie.
Vancouver was in command, outshooting New York, 36-23, overall, before Bossy connected on a 30-foot wrist shot at 16:43 into the third period to send the game into overtime.
After a scoreless first period, the Islanders' Mikko Makela scored at 1:37 of the second period. He took a pass from Denis Potvin along the boards and fired a 25-foot slap shot from inside the circle, beating goalie Frank Caprice, who was making his first start this year.
Steve Smyl tied it for Vancouver on a power-play goal at 9:51 of the second period. Tomas Gradin knocked the puck out from behind the net to Smyl in the slot and the Vancouver captain put a 10-footer past goalie Kelly Hrudey.
The Canucks scored a go-ahead goal at 12:52 of the second period. Smyl's miss from about 30 feet caromed over to Gradin, who put a shot past Hrudey from barely inside the circle, about 12 feet.
The Islanders tied on Bossy's fourth goal of the season, a shot that skidded under Caprice's legs.
Hrudey made 34 saves in remaining undefeated in his career against the Canucks, 3-0-1.
Islanders' Coach Al Arbour said: "You've got to look on the bright side. We got a point and we finished strong. At least it didn't go into the loss column."
After the game, the Islanders announced an injury to Brent Sutter has been diagnosed as a bad bruise and slight strain to his right shoulder and he will be out two weeks.