The teams duplicated their game at Miami Arena on October 13, which also ended in a 2-2 tie. Fichaud was in goal for that game, too.
He and the Islanders were rescued by the crossbar at the end of regulation when Florida's Johan Garpenlov had a chance to win the game, but his shot grazed the crossbar with 24 seconds left.
"I was trying to lift it, but not that high," Garpenlov said. "I was aiming for just above the middle of the net."
Despite being outshot 39-20, the Islanders salvaged a tie behind second-period goals by Travis Green and Robert Reichel.
New York had a potential game-winning goal waved off with 2:25 left in regulation. Green's blast grazed the left post and was disallowed after being reviewed.
The Panthers had another opportunity in overtime, but Ray Sheppard's shot hit the right post with 2:05 left.
"We dominated the whole game, and then they tie it up on their ninth shot on goal," Florida coach Doug MacLean said. "We had 30 shots at the time. I don't know if we can play any better than that.
"The game should have been over halfway through, but they get a power-play goal and then another goal on a broken play. Still, I thought it was one of our best 60 minutes of the year."
The Panthers led 2-0 -- and that wasn't a good sign. They're now 0-1-3 in games when they take a 2-0 lead.
"We're definitely having trouble closing," said Florida's Bill Lindsay. "We've had games where if we got that third goal, we would have sealed the game. We have to start finishing these games better."
The Panthers led 2-0 in the first period on goals by Ray Whitney and Lindsay. The Panthers outshot the Islanders 17-3 in the period.
Whitney scored on a four-on-three power play, sending a backhand past Fichaud at 8:25 of the period. For Whitney, it was his second goal in just three games with the Panthers. He joined the club on November 6 after being released by Edmonton.
Lindsay put Florida ahead 2-0 with a one-timer from the bottom of the right circle with 1:50 left in the period.
Despite being outshot 28-10 through two periods, the Islanders managed to tie it.
Green's power-play goal was set up by Zigmund Pallfy. Green took Pallfy's pass and rifled it past the left shoulder of John Vanbiesbrouck at 11:51.
Reichel then dug the puck out from behind the boards and sent it out front to Mariusz Czerkawski, whose blast missed, but Reichel was there to bury the rebound at 12:17.