Playing with Kyle Connor and Byran Little helped. The line combined for nine points; Connor had a goal and three assists, giving him nine points (four goals, five assists) in a five-game point streak, and Little had a goal and an assist.
"We have three good players on that line," Laine said. "I always liked playing with those two, and we are starting to build some chemistry between the three of us, and today it was just kind of clicking."
Mark Scheifele had a goal and assist, and Connor Hellebuyck made 22 saves for the Jets (12-5-2), who are 4-0-1 in their past five games.
"They had some moments where they pressed hard and put us on our heels," Little said. "But for us, the big thing was that third period, we kept in it and stayed positive."
Elias Pettersson, Tyler Motte and Nikolay Goldobin scored, and Jacob Markstrom made 43 saves for the Canucks (10-11-2), who have lost six straight (0-5-1).
"Until the end of the third, it's a tight game," Markstrom said. "But that doesn't help us much right now with the position we're in. We're in the position where we need points."
Winnipeg outshot Vancouver 23-7 in the first period.
"You hear coach talk about a shooter's mentality, and that's what we did, and it gets everybody's feet moving," Connor said. "So much creates off that first shot."
Little made it 1-0 1:13 into the game after Markstrom's errant clearing attempt left the Jets forward with an open net.
"You score on your first shift, and it seems like you got an extra gear out there," Little said.
Pettersson tied it 1-1 when he scored with a one-timer on the power play at 8:09. It was his second straight game with a goal after a four-game point drought. Pettersson leads the Canucks and NHL rookies with 12 goals and 19 points in 17 games.
Scheifele scored on the rebound of a Nikolaj Ehlers shot off the rush to make it 2-1 at 14:00, and Connor beat Markstrom 39 seconds later from a sharp angle off a rush on the power play to make it 3-1 at 14:39.
The Jets made it 4-1 at 10:04 of the second period after two Canucks collided and lost the puck to Connor, who passed to Laine alone in the slot.
Winnipeg's NHL-leading power play (32.1 percent) had a chance to extend the lead after a penalty on the ensuing face-off, but Motte scored on a shorthanded breakaway to make it 4-2 at 11:21.
After Pettersson's pursuit forced Winnipeg defenseman Tyler Myers into a turnover, Goldobin drove to the net and deked around Hellebuyck to score on his backhand to get Vancouver to within 4-3 at 16:08.
"We felt comfortable, started playing faster, created more chances," Goldobin said.