Nate Schmidt, J.T. Miller and Nils Hoglander scored early to help the Canucks end a four-game losing streak (0-3-1).
All three goals came from shots inside the blue line that were tipped, redirected or knuckled past Winnipeg goaltender Connor Hellebuyck.
''When you know you can get yourself into those areas, that's where the goals are scored,'' said Schmidt. ''I was proud of our guys for how we got to those areas tonight.''
Elias Pettersson added an empty-netter.
''I think top to bottom we had some good efforts tonight,'' Canucks coach Travis Green said.
Hellebuyck had 15 saves for Winnipeg, which snapped a four-game winning streak.
The teams finish their two-game series Tuesday night in Winnipeg.
''You've got to have a short memory in this league,'' the Jets' Mark Scheifele said. ''You can't dwell on things too long. You've got to get a good sleep tonight and get ready for tomorrow.''
After being held to one shot on goal over the first eight-plus minutes, Schmidt sent a fluttering shot from the high slot past a screened Hellebuyck at 8:28 of the first.
A similar play just 18 seconds later doubled Vancouver's lead. This time Schmidt's point shot was redirected by Miller.
Vancouver's second power-play unit used the same formula to extend the lead at 14:50. Tyler Myers sent a wrist shot from inside the blue line that Hoglander tipped to make it 3-0.
Demko, meanwhile, was steady if unspectacular in the Vancouver net, giving up few rebounds and coming through when needed.
''I think over the last handful of games, our defensive side of things is coming along really nicely,'' Demko said. ''Tonight was kind of the pinnacle of building up to this point.''
The Jets, who fell to 8-4-1 at home, seemed more inspired in the second period but had difficulty delivering any sustained pressure.
Winnipeg pressed at times in the third. Scheifele had two decent chances midway through the period and Blake Wheeler was denied after a crafty deflection on a shot by Sami Niku.
The Jets pulled Hellebuyck with over five minutes left in regulation. Winnipeg hit the post on a deflected shot but Pettersson put the game away at 16:26.
The Canucks had 19 shots on goal and improved to 4-8-0 on the road.
After Tuesday's game, the Jets will take to the road for 12 of their next 14 games.
The Canucks will return home to kick off a five-game homestand Thursday against the Toronto Maple Leafs.
Winnipeg remained in third place in the North, one point behind Edmonton.
Vancouver, sixth in the North, pulled three points behind fourth-place Montreal. However, the Canucks have played five more games than the Canadiens.
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