Motte scored on a breakaway at 9:34 of the second period to make it 2-0, and again on a slap shot through a scramble at the top of the crease at 9:45 to extend the lead to 3-0. It was his first multigoal game in the NHL.
"I was just happy to get two chances," said Motte, who had gone 17 games without a point. "My game is pretty simple: be competitive, be hard working, be physical, be responsible in the D-zone. And I've been able to chip in a little bit offensively. That's not the bread-and-butter of my game, but it's nice to do it."
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Brock Boeser and Jake Virtanen also scored, and Jacob Markstrom made 21 saves for the Canucks (29-32-9), who won in regulation for the second time in 18 games (5-10-3, with one OT win, two shootout wins).
Vancouver is eight points behind the Arizona Coyotes for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"We talked about responding and I thought we did that," said Markstrom, who was pulled from his last start. "It was a really good game for us through 60 minutes."