So they settled things in a shootout.
"The result was the most important thing," Vokoun said. "I think we played good for part of this game but we have to do it for 60 minutes."
Tim Jackman, Trent Hunter, John Tavares and Kyle Okposo had the goals for New York. Roloson stopped 38 shots for the Islanders, who played for the third time in four nights. New York (7-6-7) won at Carolina in overtime on Friday night.
Okposo could have forced a fifth shootout round after Horton scored, but Vokoun made the save. Okposo's power-play goal at 15:14 of the third period moved the Islanders into a 4-4 tie.
"We showed resilience in getting that point," Okposo said.
New York had a 2-0 lead following one period and Florida was up 4-2 in the third.
"Definitely it was a weird game," Horton said.
The Panthers improved to 4-1 in shootouts this season, and the Islanders fell to 1-4.
Frolik's power-play goal at 3:03 of the third gave Florida a 4-2 lead, but Tavares brought the Islanders back within a goal when he scored his eighth of the season during a power play at 8:27.
Olesz scored his fourth goal at 19:33 of the second to give Florida a 3-2 lead. He was one of four players fighting for the puck directly in front of Roloson, and the left winger managed to poke it into the net.
Earlier in the second, Stillman and Weiss scored 31 seconds apart to erase New York's early 2-0 lead. Stillman scored his fourth at 10:21 with a high wrister from the left circle. Weiss took a pass at center ice from Horton, skated in on the left side and beat Roloson high for his fifth goal.
Jackman and Hunter staked the Islanders to the two-goal lead in the first. Jackman scored his second goal 16 second in when Nate Thompson fed him a pass from behind the net.
Hunter scored at 4:29 when he took a pass from Josh Bailey in the high slot and fired a shot past Vokoun. It was Hunter's third goal.
"Sometimes when you get a lead like that, you get a little lackadaisical," Tavares said. "You have to bear down and be sharper."
New York earned at least a point in a third straight road game for the first time since Jan. 13-22, 2008. ... The Islanders fell a goal shy of becoming the first team since Pittsburgh in October 1992 to score three first-period goals in four straight games.