After the Canucks tied the game 2-2 at 10:52 of the third on Sedin’s 24th of the season that he banked in off Greiss from the corner, Hickey scored his fourth on a blast from the point just 2:03 later that appeared to hit a defender in front.
Vancouver pulled Markstrom with 2:30 to go in regulation, but the Canucks were unable to find an equalizer despite some sustained pressure.
The Islanders sit third in the Metropolitan Division, while the Canucks remain eight points out of a playoff spot in the Western Conference.
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 moved to either Chicago or Dallas, but Canucks general manager Jim Benning was 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 Canucks net that Lee tipped off Vancouver's Ben Hutton and just over the line past Markstrom's outstretched glove for his 10th goal of the season.
The Canucks nearly got back to level terms moments later, but New York's Calvin de Haan swept the puck off Greiss' goal line following a scramble in front.
Vancouver had a 3-on-1 earlier in the period that didn't even result in a shot before New York went the other way on a 2-on-1, with Brock Nelson hitting the post behind Markstrom.
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.
Vancouver got that one back on the power play at 10:42 when Vey scored his third from the slot on a rebound.
Notes: Islanders forward Shane Prince, acquired from Ottawa before Monday's trade deadline, made his debut for New York. ... Canucks forward Radim Vrbata, the other veteran unrestricted free agent rumoured to be on the way out of town at the deadline, sat out a third straight game with a lower-body injury. ... Jannik Hansen also missed out for Vancouver with an undisclosed injury.