Kyle Connor scored for the Jets (28-23-3), who have lost nine of their past 10 games and are one point ahead of the fourth-place Montreal Canadiens. Laurent Brossoit made 28 saves.
"I think when you go through a stretch like we're going through right now, it's very frustrating," Winnipeg captain Blake Wheeler said. "I still think we have a good vibe in our room and a lot to look forward to going forward, but we are certainly having a hard time here closing out the season."
Nils Hoglander scored twice, and Thatcher Demko made 39 saves for the Canucks (21-26-3), who were eliminated from Stanley Cup Playoff contention when the Canadiens clinched the final berth from the North by earning one point in a 4-3 overtime loss to the Edmonton Oilers on Monday.
"I think we knew the odds were stacked here for the last few games, so I think the team is probably prepared for that," Vancouver coach Travis Green said. "When you start a season, you want to make the playoffs. But when it's official, it always stings a little bit."
Hoglander gave Vancouver a 1-0 lead when he scored on his own rebound at 3:04 of the first period after a turnover by Jets defenseman
Ville Heinola
at the Canucks blue line.
"I think I played great tonight," Hoglander said. "I had a lot of chances, but I think I can score more goals if I [capitalize] on my opportunities."