Vancouver got on the board less than two minutes in and kept up offensive pressure that overwhelmed the Panthers much of the game.
Brian Boyle and Mike Hoffman scored for Florida, but the loss snapped an eight-game point streak (4-0-4).
Canucks goalie Thatcher Demko made his fourth start of the season and stopped 27 shots.
BUFFALO, N.Y. (AP) — Nick Schmaltz scored in the shootout, leading the Coyotes to the road win.
Conor Garland and Carl Soderberg scored in regulation for Arizona (7-3-1). Darcy Kuemper made 24 saves and stopped all three Sabres attempts in the shootout.
Schmaltz scored the game-winner on a low shot to the glove side.
Jack Eichel and Jeff Skinner scored for Buffalo (9-2-2), which had won four of five. Carter Hutton made 41 saves.
The Coyotes dominated the last part of the game, outshooting the Sabres 30-15 over the final two periods.
Both teams had prime scoring opportunities in overtime. The Sabres hit the post twice, and Arizona's Clayton Keller nearly found himself with an empty net after Hutton mishandled the puck.