Sam Montembeault was pulled after giving up three goals on nine shots in the first 6:18. Brian Boyle and Mike Hoffman scored for Florida (5-3-4), which was 4-0-4 in its previous eight games. The Panthers are 1-1-1 on a four-game road trip.
"I don't think we were ready to play," Florida coach Joel Quenneville said. "They were the more desperate team by a wide margin, and right off the bat. Tough to catch up from 3-0 from the drop of the puck."
WATCH: [All Panthers vs. Canucks highlights]
Montembeault returned at the start of the second period and finished with 25 saves. Sergei Bobrovsky, who made 24 saves in a 6-2 win against the Edmonton Oilers on Sunday, allowed two goals on six shots.
"We went completely from the best game of the season to probably the worst," Panthers captain Aleksander Barkov said. "It was 2-0, 3-0 like before we could even start playing and it's tough to come back in this league."
J.T. Miller scored two goals, and Elias Pettersson and Alexander Edler each had three assists for Vancouver (7-3-1), which is 7-1-1 in its past nine games.
All four forward lines scored early in the first period for the Canucks, who have scored five or more goals in three straight games for the first time since Dec. 1-6, 2011.
"If you want to build a playoff team, go deep in the playoffs, you're going to have to have a bunch of guys throughout the lines that can score, and you're seeing that," said Vancouver goalie Thatcher Demko, who made 29 saves. "That's huge for us to have some depth with our scoring."