Ryan Pulock scored for the Islanders at 8:06, but the goal was overturned after the Panthers challenged for goaltender interference.
Duclair knocked down a stretch pass from MacKenzie Weegar at Florida's offensive blue line and deked to his backhand for a breakaway goal and a 3-0 lead at 18:57.
"I was shocked why he didn't use his hand," Panthers coach Joel Quenneville said. "The way he took it off his tape there was an unbelievable play. The great play was [Duclair] taking the pass, staying onside, being in stride and making the finish as well. We'll give a little credit to [Weegar]."
The Islanders outshot the Panthers 20-13 through two periods.
"I thought we were really good in the first two periods," New York coach Barry Trotz said. "They didn't have very many scoring opportunities, but when we've been breaking down, we've been really breaking down in some areas. We probably didn't deserve to be down 3-0 after two periods."
Wahlstrom cut it to 3-1 when he gathered a loose puck below the left face-off circle and scored a power-play goal at 3:30 of the third period.
Bennett completed the hat trick when he carried the puck through the neutral zone and scored on a wrist shot from the high slot to make it 4-1 at 9:39. Matt Kierstad got the assist for his first NHL point.
Barkov made it 5-1 at 12:22 when he cut to the slot and flipped the puck in.
"No matter what line we put on the ice, the objective is to play offense, keep the puck and play in their end," Quenneville said. "Any line can score. Tonight, we did a lot of good things."
NOTES: Huberdeau has 168 goals and 332 assists in 593 games. … Bennett's only other NHL hat trick came when he scored four goals for the Flames in a 6-0 win against the Panthers on Jan. 14, 2016. … Defenseman Zdeno Chara was minus-4 for the Islanders. … It was the second of 13 straight road games to start the season for New York, which debuts at its new home, UBS Arena, against Calgary on Nov. 20.