Green, who has just one regulation goal in 37 games this season, beat Florida goaltender Ed Belfour with a forehand shot to extend Vancouver's unbeaten streak to seven games. Green admitted he was surprised when coach Alain Vigneault sent him out as the sixth shooter in the shootout.
"I felt the kick in the back and thought someone was playing a joke on me," said Green, whose only other goal this season was the winner in a Nov. 19 game against Chicago.
"I didn't even have time to think. I knew I wanted to get a good shot away. I'm just trying to get my heart rate down a little bit. It was nerve wrecking but I'm glad it worked out."
Canuck goaltender Roberto Luongo made some great saves, but also gave up a couple of soft goals in his first game against Florida since the June 23rd trade that saw him come to Vancouver in exchange for forward Todd Bertuzzi.
A back injury kept Bertuzzi out of the game and had dampened some of the fans' enthusiasm for one of the most anticipated matches of the season.
"I was a little nervous at the beginning," said Luongo, who made 33 saves in 65 minutes, and then five more in the shootout.
"I felt pretty good the whole game and then lost a bit of energy in the third (period). The important thing is we got two points."
It was the second time in three games Vancouver was forced into a shootout. The Canucks beat Dallas 2-1 on Wednesday and is now 3-1 in shootouts.
It was the third consecutive loss for the Panthers, who also dropped an overtime game to Calgary Thursday night.
"We need all the points we can get right now," said Mike Van Ryn, who scored on a sharp-angle shot from the boards to give Florida a 2-1 lead in the third period.
"We're just having problems closing out these games. I don't know if it's nervous or what."
It was a game that the Canucks almost let get away.
The Panthers forced the overtime with Gregory Campbell's short-handed goal at 11:35 of the third.
The Canucks looked to have the match won when Brendan Morrison scored off the rebound of a Markus Naslund shot for a 3-2 lead midway through the period.
Naslund had tied the game 2-2 at 3:59, scoring from a scramble. The goal broke a 17-game scoring drought and earned the Canuck captain a standing ovation from the sellout crowd of 18,630.
Naslund celebrated by pumping both fists in the air.
"I don't usually show a lot of emotion when I score but when you do it every 17 games, you might have to," he said.
Trevor Linden also scored for the Canucks on a first-period power play.
Ville Peltonen got the other goal for the Panthers, who haven't won in Vancouver since March 7, 1994.
Vancouver improved it's Northwest Division-leading record to 24-18-1. Florida is last in the Southeast Division with a 15-20-9 record.
While Bertuzzi and Luongo were the principles in last summer's blockbuster deal, three other players were involved.
Defenceman Lukas Krajicek came to Vancouver while defenceman Bryan Allen and goaltender Alex Auld went to Florida.
Allen was the only former Canuck who played Sunday.
Bertuzzi, who underwent back surgery in November, has played just seven games this season. Auld, who began the season as Florida's starter, lost his job to Belfour.
After a slow start, the Panthers took the game to the Canucks. Florida looked especially strong in the second period, where at one point they had outshot Vancouver 11-1.
The Panthers showed more team speed, quickly moving the play up ice and pouncing on loose pucks.
Vancouver's Ryan Kesler and Florida's Steve Montador scored in the first phase of the shootout, forcing it to the sudden-death round.
Panther captain Olli Jokinen was one of the players who couldn't beat Luongo.
"We had three chances to put the game away in the shootout and we didn't score," said Jokinen. "It's sad. A tough loss.
"I was going against my good friend (Luongo). I had a dream about that last night. In my dream, I scored."
As he's done all season, Luongo made some big saves to keep the Canucks in the game. He got a glove on a shot from Rostislav Olesz on a two-on-one breakaway in the first period, then twice stopped Jokinen in the second
Notes: Linden's goal was his fifth in 11 games. ...Jeff Cowan had four hits in the first period. ...Coach Alain Vigneault says Luongo could play over 75 games this year.