VANCOUVER – The New York Islanders know they got away with one.

Thomas Hickey scored the winner in the third period and Thomas Greiss made 31 saves as New York defeated Vancouver 3-2 on Tuesday in a game where the Islanders had just nine shots through 40 minutes and saw all three of their goals go in off Canucks defencemen.

“The positive thing is you end up winning it,” said Hickey, who also added an assist. “But to a man in here I think we all understand that’s not going to win too many hockey games. Our goalie sort of bailed us out there and we got lucky.”

Travis Hamonic and Anders Lee also scored for New York (34-20-7), which moved to within five points of the Rangers for second in the Metropolitan Division and three up on fourth-place Pittsburgh.

“It was a pretty gritty win on the road,” said Lee. “They poured it on us a little bit.”

Linden Vey and Daniel Sedin replied for Vancouver (24-26-12), which got 21 saves from Jacob Markstrom. The Canucks remain eight points out of the final playoff spot in the Western Conference and barring a miracle will miss the post-season for the second time in three years.

“We had a few bad breaks tonight. It’s a tough one,” said Vancouver head coach Willie Desjardins. “I thought our team played well. I thought we worked real hard. We deserved better.”

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After the Canucks tied the game 2-2 at 10:52 of the third on Sedin’s 24th of the season, Hickey scored his fourth on a blast from the point just 2:03 later that went in off the stick of Vancouver’s Christopher Tanev.

“Same story again. We battled hard all game,” said Canucks captain Henrik Sedin. “You can’t be (anything) but proud of the guys.”

Dan Hamhuis suited up for Vancouver a day after the NHL trade deadline came and went without a deal for the veteran defenceman.

Hamhuis — who has a no-trade clause in his contract and is set to become an unrestricted free agent this summer — agreed to be moved to either Chicago or Dallas, but the Canucks were unable to get anything done before the 3 p.m. ET cutoff.

Tied 1-1 after the first period, the Islanders grabbed the lead with 5:30 left in the second on a goal that required video review. Hickey threw a shot towards the net that Lee tipped off Vancouver’s Ben Hutton and just over the line past Markstrom for his 10th.

The Canucks, who had a number of chances in the period that Greiss turned aside, nearly got back to level terms moments later, but New York’s Calvin de Haan swept the puck off the goal line following a scramble in front.

The Islanders opened the scoring at 4:20 of the first on their first shot when Hamonic threw a puck on net from the sideboards that deflected off Hamhuis’ stick and past Markstrom for his fifth, but Vancouver replied on the power play at 10:42 when Vey scored his third.

Henrik Sedin, who lined up alongside Daniel Sedin and Emerson Etem on the Canucks’ top line after Jannik Hansen was injured in the morning skate, said it’s important his team continues to battle the way it did on Tuesday over the final 20 games of the schedule.

“You’ve got to look at the big picture,” he said. “That’s to realize where we are as a team with the (young) guys we have. You’ve got to look forward and try to come in every day and teach and be positive and try to get better. We can’t lay down flat and just play out the rest of the season.

“We know we want to create a culture where it’s not good enough to lose, and that’s what we’re trying to do even though there’s been a lot of losing.”

Notes: Desjardins said Hansen suffered a rib injury and will be re-evaluated in a week. … Canucks forward Radim Vrbata, the other veteran unrestricted free agent rumoured to be on his way out of town at the trade deadline, sat out a third straight game with a lower-body injury.