Scott Walker, Cory Stillman and Justin Williams also scored, and Eric Staal added two assists for Carolina. Williams' goal was his team-leading 18th of the season and seventh in seven games.
Nathan Horton scored two goals for Florida, and his second cut it to 3-2 with 4:11 remaining.
Florida pulled goalie Alexander Auld in the final minute, but Stillman made them pay by scoring an empty-net goal on a backhand from the blue-line while falling down with 40 seconds left.
Cam Ward made 28 saves for the Hurricanes, who won their seventh straight home game against Florida.