Chris Wells and Scott Mellanby had the other goals for Florida, which improved to 2-3 on its six-game homestand and moved four points ahead of the fifth-place New York Rangers in the Eastern Conference.
The Panthers had not posted consecutive wins since February 9th-12th.
Lonny Bohonos tallied twice in the third period for Vancouver, which had an apparent go-ahead goal disallowed in the second period and is winless in seven straight games (0-5-2). The Canucks trail Calgary and Chicago by five points for the final Western Conference playoff berth.
With the score tied, 2-2, a turnover behind the Florida net led to Bret Hedican's goal with 12 minutes remaining. But it was disallowed after video replays showed that Vancouver teammate Martin Gelinas had part of his skate in the crease.
"I thought it was the worst call I've ever seen since I've been in the league," Hedican said. "His toecap was in the crease. We were playing against two opponents, the Florida Panthers and (referee Mark) Faucette. He did a terrible job. Even the penalty shot was a terrible call. Life isn't easy and we have to back each other up and battle through it. We're just not getting any breaks."
"I'm not one to question officiating, I never do it. But you can't beat the other team and the referee," added teammate Mike Sillinger. "Martin wasn't close to (goaltender John) Vanbiesbrouck. The Panthers didn't complain, so he didn't have to review it."
Even Vanbiesbrouck seemed to agree.
"The best goal of the game is the one they called back," he said.
The Panthers took advantage of the call and took a 3-2 lead when Wells stuffed home a rebound of Mike Hough's shot at 8:24. It was Wells' second goal of the season and first since February 12th.
"We played two real good periods and the third, we didn't do as well and it wound up hurting us. Obviously, the turning point was the disallowed goal and Chris Wells' goal after that," said Florida coach Doug MacLean.
Canucks goaltender Corey Hirsch stopped Rob Niedermayer on a penalty shot less than two minutes later, but Sheppard tallied twice in a 2:46 span later in the period to complete his 11th career hat trick and extend Florida's lead to 5-2.
"I got some bounces. Fortunately, they went in for me," Sheppard said. "We were poised against the Islanders and it carried over to tonight. It's not 500, but hopefully I'll get there one day. When I started playing, I had three goals. One was to make it to the NHL. Number two was to play on a Stanley Cup winner and number three, to have some individual success."
That enabled the Panthers to survive a pair of third-period goals by Bohonos, who has three in as many games.
Mellanby and Sheppard scored 84 seconds apart midway through the first period to stake Florida to a 2-0 lead. But Gelinas got Vancouver on the board at 16:01 and Markus Naslund was credited with the tying goal at 19:17 when Sillinger's backhander from the right faceoff circle deflected into the net off his face.
Gelinas, who put a bearhug around Niedermayer to stop his breakaway, objected to Faucette's decision to award a penalty shot.
"He got off a shot, so how can they call it a penalty shot?" he asked. "Everyone in this room still believes. The referee was more on the other side than on our side, so we're getting no breaks. We have to play through tough times and injuries."
Jon's 3 stars:
1. Ray Sheppard
2. Radek Dvorak
3. Rob Niedermayer