The Canucks won their fourth straight game, 3-2, and the Oilers lost left wing Taylor Hall to a leg injury early in the second period.
Vancouver right wing Derek Dorsett's shorthanded goal at 4:05 of the third period was the game-winner and gave the Canucks their third victory of the season against Edmonton.
Dorsett, who was acquired in a trade with the New York Rangers in the offseason, intercepted an errant clearing attempt by Oilers goaltender Ben Scrivens off the right-wing boards and snapped it in on the short side for his first goal with Vancouver.
"Every goal is important, but it was exciting to get my first goal as a Canuck," Dorsett said. "It just so happened to be the winner and shorthanded as well, which made it that much better. I saw him cheating a bit and just threw it on the net."
Hall was injured when he lost his balance on a rush off the right wing and went crashing into the Canucks net, hitting his right leg on the goal post before sliding hard into the end boards.
"I have no update on Taylor yet," Oilers coach Dallas Eakins said. "Obviously it's always going to be a huge hole to fill when that young man leaves your lineup."
Hall leads the Oilers in scoring with six goals and three assists.
Scrivens took responsibility for the turnover that led to Dorsett's game-winning goal.
"I made a bad play, that's about it," said Scrivens, who made 27 saves. "It's unbelievably frustrating. To make a play that cost your team the game is unbelievably frustrating. You have to try not to make those."
Jordan Eberle and David Perron scored for the Oilers, who are winless (0-6-1) against Western Conference opponents this season. The Oilers are undefeated (4-0-0) against teams from the Eastern Conference.
Goaltender Ryan Miller made 25 saves for his eighth win. He is 10-0-0 lifetime against the Oilers.
"It's just kind of how it worked out," Miller said. "When I was out East [Buffalo Sabres], you would face teams like them maybe every other year, and a lot of the games they were on a long trip coming into our building. It's just one of the anomalies of the game. I prepare the same for any team. Every game has been close this season. It's just been a matter of having that last little push at the end for us."
Eberle gave the Oilers the lead at 12:39 of the first period, taking a pass from Hall on the wing and managing to squeeze a one-handed backhand shot through Miller.
Sbisa tied the game with 47 seconds left in the period, getting to a loose puck in front of the net and snapping it past Scrivens. Vey scored at 16:37 of the second, powering a rebound past Scrivens for a 2-1 Vancouver lead.
"Our start wasn't the best," Sbisa said. "They were outplaying us and shooting pucks from everywhere, which threw us off balance. But as the game went on we got better and better."
Perron tied the game 2-2 at 17:41, taking a pass from Leo Draisaitl and beating Miller with a wrist shot. The goal was Perron's first of the season. He and Eberle tied for the Oilers lead in goals last season with 28.
"We wanted to get that win for [Scrivens]; he made a real good save after on [Daniel Sedin and Henrik Sedin] on a 2-on-1," Perron said. "He's been playing well all year. That goal is probably one he would like back, but we're a team in here, and I thought it was a really good effort. Our pace and our energy was good, and it was really frustrating not getting those two points tonight."
Dorsett's shorthanded goal was the first of the season for Vancouver, and the second allowed by Edmonton.
Eakins defended Scrivens, who made his eighth straight start.
"I'm certainly not going to stand here and crucify the guy," Eakins said. "It's easy to stand back and point fingers, but that kid kept us in that game and made a lot of key saves. He was a huge part of us coming out of the hole when we hadn't won. He'll bounce back, he made a mistake, he's owned up to it. He kept us in the game with some massive saves. I'm very cautious to pin the whole game on him."
The Oilers begin a five-game road trip Tuesday at the Philadelphia Flyers. The Canucks host the Nashville Predators on Sunday.