Andrei Kuzmenko had a goal and an assist for the Canucks (16-16-3), who had won three straight and their previous seven road games. Collin Delia made 35 saves.
"I think [Winnipeg] had a little more jump," Vancouver forward Curtis Lazar said. "We didn't execute as clean, especially in our own end. Puck battles were a big thing, bearing down on each blueline. Also, our willingness to get in the dirty areas and in both the [defensive] zone and the [offensive] zone."
Elias Pettersson intercepted a Dylan Samberg pass and set up a one-timer for Kuzmenko to give the Canucks a 1-0 lead just 41 seconds into the first period.
"We were happy with the way we started, coming in ready to play, but just couldn't follow it up with anything good in the second and third," Vancouver captain Bo Horvat said. "We kind of sat back and got comfortable, and that's the result that happens. We took a couple of unfortunate penalties and they capitalized on those."
Scheifele tied it 1-1 at 13:52 of the second period on the power play, tipping a Morrissey point shot that bounced off the ice before going past Delia.
"We started skating again," Bowness said. "I think that early goal against kind of set us on our heels a little bit. And that team has been playing really well lately, so they were feeling it. Sometimes you've just got to play through it, and we were able to do that tonight. That team, they had won what seven in a row on the road. So, we had to play through it, and we did."
Dubois was awarded a penalty shot at 15:42 when he was hooked on a breakaway by Ethan Bear. Dubois scored with a wrist shot stick side to give the Jets a 2-1 lead.
"We started to focus a little too much on defense and not on offense at all," Canucks coach Bruce Boudreau said. "The last five minutes [of the second period], they started to gain some momentum and they're a good shut-down team and they've got a good goalie."