Josh Morrissey (9:04, first period) and Nikolaj Ehlers (empty net) scored, and Bryan Little had two assists for the Jets, who were outshot 12-6 in the second period but scored the only two goals.
Laine scored his second goal of the season on a quick shot from the slot at 15:31, and Myers scored on a 2-on-1 to make it 3-1 at 18:44.
"Simplicity," Myers said of the difference the last two games. "We're not trying to get too cute when things aren't going our way. That's a habit we have to start creating to where it becomes second nature for us."
Canucks defenseman Chris Tanev made it 3-2 with a fluttering point shot that somehow eluded Hellebuyck's glove at 12:43 of the third period, but Vancouver couldn't tie it despite outshooting Winnipeg 12-5 in the period.
"I'm not going to be playing baseball anytime soon," Hellebuyck said. "That was tracking to my glove and I don't know why I went down, that was my mistake and I kind of blinded myself. You don't see many pucks move from one end to the other."
Daniel Sedin (7:25, first period) scored a power-play goal, and Jacob Markstrom made 16 saves for the Canucks (1-1-1), who lost defenseman Alexander Edler to a lower-body injury in the first period.
"He's our minute-logger, plays in every situation," Tanev said. "It's tough to lose him and play with five the rest of the game."