Jonathan Marchessault's 10th goal of the season gave Florida a 1-0 lead at 5:40 of the first period. With the Panthers on the power play, Jaromir Jagr got a stick on Barkov's shot, but Marchessault cleaned up a rebound on the backhand.
Ekblad made it 2-0 on an unusual play. Leighton initially caught Barkov's shot, but when the Hurricanes goaltender bobbled the puck, Jagr used his stick to tap Leighton's glove and knock the puck over Leighton's shoulder and into the net at 9:51.
"You could tell both teams played [Saturday] night," Hurricanes coach Bill Peters said. "They skated a little better than us early, and once we got skating we looked a little better."
The Hurricanes started their comeback when Victor Stalberg made it 2-1 at 5:21 of the second period. Matt Tennyson sent a backhand feed to Stalberg at the top of the crease, where he beat James Reimer between the legs.
Jeff Skinner tied the game 2-2 with a breakaway goal at 7:12. He took a pass from Victor Rask and held off Aaron Ekblad before finishing a backhand under the crossbar.
Derek Ryan made it 3-2 with his first of the season on the power play at 8:49. Ryan won an offensive zone draw to Skinner, whose shot was poke-checked by Reimer. Ryan quickly gathered the puck and scored on the short side.
"For five minutes we let them come back in the game and they scored three goals," Gallant said. "That was disappointing because we played 55 good minutes tonight, but it wasn't enough."