Noah Dobson scored for the Islanders (20-23-8), who have lost four of five and began a six-game homestand. Semyon Varlamov made 34 saves.
"This one hurts," New York center Brock Nelson said. "Coming back after a long trip, everybody excited to be home … I thought we had a good first (period), a little sloppy in the second, and then we found a way to have the lead in the third. You'd like to think that we could hang on to it, but a couple of plays, quick plays, that was the difference. Turnovers kind of led to some of their offense."
Anthony Beauvillier gave the Islanders a 3-2 lead at 1:49 of the third period. He stole the puck from Brock Boeser in the slot, deked Demko and had his shot trickle over the goal line off the stick of the Canucks forward.
Hoglander tied it 3-3 at 9:34 when he redirected Conor Garland's feed in the low slot, and Podkolzin put Vancouver in front 4-3 at 10:19 with a one-timer off a backhand pass from Bo Horvat, who warded off Scott Mayfield to make the play.
The goal ended a 20-game drought for Hoglander, who hadn't scored since Jan. 1.
"It's awesome," Boeser said. "Obviously, he's a young guy (21 years old) and it's probably the longest he's gone without scoring, but it's just something you've got to work through, and you get out of those slumps by hard work. He stuck with it."
Demko preserved the lead with 1:21 remaining with a save on Jean-Gabriel Pageau's wrist shot from the edge of the left circle.
Dobson gave the Islanders a 1-0 lead at 3:37 of the second period when he one-timed Nelson's pass from the right point. It was his 10th goal of the season.
Brad Hunt tied it 1-1 at 7:19 on a one-timer following a giveaway by Sebastian Aho that trickled past Varlamov. It was his first goal this season in his 25th game.
"There's an old saying, 'Turnovers are like ex-wives. If you have too many, they cost you a lot, and they cost you more and more,'" Islanders coach Barry Trotz said. "It's so true, and that was the second period."
Hunt, a native of Maple Ridge, British Columbia, is in his first season with Vancouver after signing a one-year contract last offseason.
"It feels great," the defenseman said. "Never would I have ever dreamed of playing for my hometown team and scoring a goal and getting a huge win when we need it the most. It's obviously a great feeling."