Miroslav Satan, Jason Blake and Alexei Yashin also scored for New York, 3-0-1 on its five-game road trip.
Ville Peltonen had the only goal for the Panthers, and Ed Belfour made 29 saves.
Blake's goal at 16:23 of the third period gave the Islanders a 3-1 lead. Yashin took the puck away from Olli Jokinen along the boards and passed from the right circle to Blake, who slid the puck by Belfour from in front. Blake leads the Islanders with 10 goals.
Satan had an empty-net score at 19:19.
New York took a 2-1 on Asham's goal at 14:19 of the second. Sean Hill's shot was blocked by Belfour but Asham picked up the loose puck and pushed it in. It was Asham's first goal of the season.
Florida tied it 1-1 at 2:26 of the second. Juraj Kolnik's shot hit Dunham's left skate and bounced out in front of the crease. Peltonen was there for the rebound and poked in the puck. It was Peltonen's first goal with the Panthers.
The Islanders took a 1-0 lead on Yashin's goal at 11:55 of the first. Jason Blake passed from the right circle to Yashin in the slot for a wrist shot that beat Belfour on the glove side.
Notes: Yashin has eight goals and 14 assists in 18 games this season. . . . Florida's Martin Gelinas recovered from a rib injury suffered on Thursday and played in tonight's game.