Luongo allowed a few easy goals in regulation, but rookie Alex Edler scored in the sixth round of the shootout to lead the Canucks to a 3-2 victory.
"It was really important to help him out on a tough night," Edler said. "He's done the same for us so often this year. He's played so well for us all year."
Edler, a game-time decision due to back spasms, beat the Islanders' Rick DiPietro between the legs for the winner.
The Islanders were fortunate to even get past regulation time as the Canucks outshot them 45-28, with only a pair of miscues by Luongo allowing them to remain in contention.
"But what a performance in the shootout huh?" Luongo said jokingly. "At least I finished off on a positive note. The guys worked really hard tonight and that's why it would have been disappointing not to get the two points. We played hard and we played the full 60 minutes. I think we deserved the two points."
Markus Naslund and Daniel Sedin scored in regulation for the Canucks. Bill Guerin and Blake Comeau had goals for the Islanders, who got 43 saves from DiPietro.
"We were in this game for one reason, and that was Ricky," Guerin said. "He played out of his mind again. We played well in the second and third periods, but we needed to play better in the first to take the pressure off of him."
Vancouver fired 19 shots at DiPietro in the first period alone.
"It was like the Harlem Globetrotters in our end for a while in the first period," Guerin said. "It was ridiculous. We were not happy with ourselves after that."
Vancouver took a 1-0 lead midway through the first period as Naslund broke a seven-game scoreless drought with his 14th goal. Naslund had scored just two goals in last 17 games before Tuesday.
The Islanders tied it six minutes into the middle frame on a strange goal.
Guerin jumped on a loose puck deep in the Canucks zone with one of the linesman apparently signaling for a delayed offsides. But when no whistle came, Guerin fired the puck toward the net from the corner, catching Luongo offguard.
The puck went under Roberto Luongo's glove, bounced off his side and into the net for Guerin's 15th of the season. Luongo, a former Islander, appeared to lose his concentration on the play, expecting a whistle to blow when Guerin touched the puck.
It wasn't one of Luongo's better nights as the Islanders took advantage of another of his miscues early in the third period to take a 2-1 lead.
Luongo went behind his net to play a loose puck only to have it get caught up in his skates. As he turned to get back to his net he ended up kicking the puck right on to the stick of Islanders rookie Comeau, who popped it into the empty net for his second of the season.
Vancouver came right back to tie it at 2 just 82 seconds later when Sedin extended his goal scoring streak to five games with a wrist shot from the slot that beat DiPietro through the legs for his 20th of the season.
