Ilya Mikheyev scored twice, and Andrei Kuzmenko had a goal and an assist for the Canucks (11-12-3), who trailed 4-0 after the first period and again 6-5 late in the third after taking the lead.
"Our team is starting to believe they can, when they get down, still make a game of it," Vancouver coach Bruce Boudreau said. "And that's a belief that if you have, you're never out of it."
Spencer Martin allowed four goals on nine shots before being replaced by Collin Delia, who made 15 saves in his Canucks debut.
"I honestly believed the whole time," Delia said. "You definitely don't draw it up like that, but there's great parity in this League and it's the age of offense, so there's going to be scoring in these games."