The Canucks lead the best-of-seven opening-round series 3-2 and can send the defending Stanley Cup champions packing from the post-season with a win Friday night.
J.T. Miller and Jake Virtanen also scored for Vancouver. Goaltender Jacob Markstrom made 36 saves.
''(Markstrom) made like four or five great saves. I thought that was the turning point for our team,'' said Virtanen, who recorded his first career playoff goal.
''We had a lot of energy on the bench. It gave us some momentum and we just took over the second period.''
Ryan O'Reilly, with his fourth goal of the series, Brayden Schenn, and Zach Sanford scored for the Blues.
Goaltender Jake Allen stopped 26 shots and took his first loss in three starts in the series.
It was a tale of two games.
The Blues were up 3-1 midway through the second period, blasting away at Markstrom and forcing him to make some acrobatic saves. Then, the Canucks scored three unanswered goals.
Miller cut the lead to 3-2. He won a puck battle behind the net, came around the front and whacked away as Blues jostled and shoved him until the puck found its way under Allen and over the goal line.
Vancouver tied it when Virtanen, standing on the goal line to Allen's right, fired a severely sharp-angle shot that bounced off Allen's arm and in. As the seconds ticked down in the period, Motte jumped on a loose puck in the neutral zone, raced in and fired a shot low blocker side for a 4-3 lead.
Markstrom made some more point-blank saves in the third period to hold off a furious Blues charge.
Schenn said they got away from playing heavy ground-and-pound Blues hockey.
''We've got to tighten up defensively. That's how we play. That's the way we win hockey games,'' Schenn said.
''Their goalie is playing really well. We're throwing a lot of pucks at him, and he's making a lot of saves, but we'll find ways to score goals. We'll look at it and make some adjustments for Game 6.''
Motte got Vancouver on the scoresheet while short-handed in the first period when Blues defenseman Alex Pietrangelo broke his stick attempting a shot at the Canucks blue line. Motte jumped on the puck and raced in on Allen with a stick-less Pietrangelo eventually chasing him down, but Motte simply turned him inside out and fired a shot stick-side high and in.
After Motte's icebreaker, it was three straight goals for St. Louis that began when Oskar Sundqvist outworked Canuck defender Chris Tanev in the corner to deliver a picture-perfect backhand pass to Schenn in the slot for a shot high glove-side on Markstrom.
With the seconds ticking down in the first period, O'Reilly showed off some sweet hands and slick skating, going wide around defenseman Alex Edler, swooping around the net and banking the puck in off Markstrom's skate while defenseman Jordie Benn got caught standing and watching.
Sanford made it 3-1 on the power play, deking and juking through the right face-off circle and using Edler as a screen to rip a wrist shot high glove side on Markstrom.
After that it was all Vancouver.
It was a tough game for Edler. The Swedish defenseman got injured in the waning moments of the second period when Blue Jordan Kyrou fell down and his leg flew up and his skate caught Edler on the right ear. Edler grabbed his ear, skated right off the ice and down the tunnel.
The Blues were without scoring winger Vladimir Tarasenko, who has gone back to St. Louis to have his shoulder reassessed by medical staff. The Russian winger played only 10 games in the regular season before dislocating his left shoulder and undergoing surgery in October.
NOTES: The Blues did get center Ivan Barbashev back. Barbashev has not been with the team since Aug. 4, leaving to be with his family in the U.S. for the birth of their first child.
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