Mats Zuccarello scored the Rangers' lone goal in the shootout, while Aleksander Barkov and Vincent Trocheck scored.
"I thought for the most part our guys played hard, made good plays with the puck and came back three times in this game," coach Alain Vigneault said. "Unfortunately we weren't able to get it done in the shootout."
Florida jumped out to a 2-0 lead beginning with a power play goal from Jonathan Huberdeau with 15 seconds remaining in the first period. Trocheck's shot was stopped by Henrik Lundqvist, but he was unable to hold on to the puck, allowing Huberdeau to slam it home for his 22nd goal of the season.
The Panthers doubled their lead at 8:13 of the second on Frank Vatrano's third goal of the season.
Zuccarello scored his second goal in as many days when he got a piece of Neal Pionk's blast from the point. Ryan Spooner picked up the secondary assist to give him four points in his last two games, and 11 points in seven games since coming over from Boston in last month's trade.
Mika Zibanejad momentarily tied the game 17 seconds into the third when his backhand shot beat Roberto Luongo over the shoulder, but Jamie McGinn responded just 45 seconds later to put the hosts back on top, 3-2.
New York again tied it with 12:35 remaining when Hayes' wrist shot from the top of the circle found a lane through traffic in front. The goal was Hayes' fifth goal in his last six games.
Another night and another learning experience for the Rangers as they continue to integrate young players on defense, including Pionk who had two assists and John Gilmour who had one.
"That's the way you've got to play to compete," said Marc Staal. "You've got to be smart with the puck, you've got to win your one-on-one battles down low. All the little things that give you an opportunity to be in a game. I thought we did that more consistently. We've got to take that recipe and move foeward and hopefully next time we can finish it off with a win."
Lundqvist, who like his teammates was pleased with the effort, especially after Thursday's lopsided defeat in Tampa, and namely with the club's resiliency in the third period. But
"We kept battling," he said. "We kept coming back in this game and gave ourselves a chance to almost win it."
