Matthew Tkachuk scored with less than five seconds left on the game clock. Florida is thus advanced from the semifinals for the first time since 1996, when Peter Forsberg's Colorado became too difficult in the final game.
Tkachuck got behind the goal cage, slid in and found the net via the left post, causing the home crowd in Sunrise to explode.
Meets Dallas or Vegas in final
Before the goal, it looked like the game was heading for extra time, after Carolina's Jesper Fast equalized for Carolina when the third period was just over three minutes old.
But Fast's sixth playoff goal was both his and the entire team's last for this season.
In the final, either Dallas or Vegas awaits, where Vegas can secure a final spot on the night of Friday, Swedish time.