Ville Peltonen also scored twice for the Panthers. Rostislav Olesz, Gregory Campbell, Juraj Kolnik and Jozef Stumpel had the other goals while Ed Belfour stopped 28 shots.
Mike Sillinger and Ryan Smyth scored two goals apiece for the Islanders while Marc-Andre Bergeron added the other. Mike Dunham had 27 saves in his second consecutive start, both losses, in place of the injured Rick DiPietro.
Jokinen put Florida ahead 5-4 with a wraparound goal at 6:04 of the third. His second goal of the period came about a minute later with a shot from the right circle that beat Dunham and gave Florida a 6-4 lead.
Smyth's goal from in front at 17:02 pulled the Islanders to 6-5. Empty-net goals in the final minute by Stumpel and Peltonen rounded out the scoring.
The Islanders tied the score 4-4 during a power play when Bergeron's shot from above the right circle went over Belfour's right shoulder at 5:16 of the third.
Kolnik gave Florida a 4-3 lead in the second. He picked up a rebound in front of the crease and pushed it past Dunham at 7:59.
There were six goals in the first, three by each team.
Sillinger's second power-play goal of the game gave the Islanders a 3-2 lead at 16:56. Florida tied it when Campbell's shot from the left circle went in at 17:31.
Florida tied the score 2-2 on Peltonen's goal at 15:54. Peltonen skated in on Dunham and tucked the puck just inside the corner of the net.
Sillinger's power-play goal at 13:00 gave the Islanders a 2-1 lead. His shot from the left circle got by Belfour, who was out in front of the crease.
New York made it 1-1 on Smyth's first goal at 10:50 of the first.
Florida scored 1:54 into the game. A shot by Jokinen hit the post and bounced out to the slot. Olesz picked up the loose puck and beat Dunham on the stick side to make the score 1-0.
Belfour made his 23rd consecutive start for Florida, breaking the franchise record set by Roberto Luongo, who is now with Vancouver.
Notes: DiPietro missed his second straight start with a stiff neck . . . Dunham made his second start in goal since Feb.1 . . . Belfour began his consecutive games streak Jan. 20, and is 22-16-8 this season.