The Blues (40-28-5) won their fourth straight and ninth in 10 games. St. Louis is tied with the Nashville Predators for third place in the division and trail the Calgary Flames by one point for the first Western wild card into the Stanley Cup Playoffs. Nashville defeated Calgary 3-1.
"We'll figure out what happens after 82 games] and go from there," Blues goalie Jake Allen said. "We've got a good thing going and hopefully we can keep it going. ... Once 82 is done April 9, we'll see where we are."
[WATCH: All Canucks vs. Blues highlights
Magnus Paajarvi scored twice, Alex Pietrangelo had a goal and an assist, and Kyle Brodziak scored. Allen made 27 saves and is 7-1-0 in his past eight starts after losing four in a row.
"We need a lot of guys to step up, and obviously we got that from Jake, we got that from some of our top guys, and then you look at what [Paajarvi] did and other guys did as far as raising their game, and getting the goals is part of it," Blues coach Mike Yeo said. "... I thought we had a collective group effort that guys were ready to step up tonight."
Henrik Sedin scored, and Ryan Miller made 30 saves for the Canucks (29-35-9), who played the third of a five-game road trip. Vancouver trails St. Louis and Nashville by 18 points for a Western wild card.
"I thought we played OK," Sedin said. "We didn't play our best game. They've got a good team and [are] playing well right now. Going into the third being down one, that's a good spot to be on the road."