On the winning play, Brian Campbell skated into the right circle, drawing the Carolina defense. He sent a pass through the crease that was tipped by Stephen Weiss to an unguarded Versteeg, who one-timed it for the game-winner.
Sean Bergenheim and Jason Garrison also scored for the first-place Panthers, who increased their lead over Washington in the Southeast Division to eight points.
Florida improved to 6-1-5 in a streak of 12 straight homes games that have been decided by one goal.
Jose Theodore turned aside 24-of-26 shots to earn the victory.
Cam Ward made 22 saves for Carolina.