Stephen Weiss' shot from in front was blocked, but Versteeg found the loose puck and swept it in from the left side of the crease for his team-leading 16th goal of the season.
Florida tied it 2-2 on Garrison's power-play goal in the third period. Garrison's shot from the point hit Ward's pads and trickled into the net at 5:47.
Carolina had taken a 2-1 lead at 13:45 of the second. LaRose got the puck away from Versteeg as he brought it out from behind the net, and his wrister from the left circle went over Theodore's right shoulder.
The Panthers went ahead 1-0 on Bergenheim's first-period goal. Ed Jovanovski's shot went off the end boards and bounced out to Bergenheim, whose shot beat Ward at 4:16. It was Bergenheim's third goal in two games and fifth in nine contests. Jovanovski had gone 16 games without a point.
The Hurricanes tied it at 1 when Gleason scored at 18:38 with a wrist shot from above the left circle that went between Theodore's pads. It was Gleason's first goal since Nov. 17, 2010 — a span of 97 games.
NOTES: Panthers 30-year-old center Greg Rallo was called up from San Antonio of the AHL on Saturday and made his NHL debut. Rallo is the second 30-year-old player to debut with the Panthers this season. Bracken Kearns played his first NHL game on Oct. 20 against Buffalo. ... Bergenheim left the game in the second period because of a lower body injury and didn't return. ... D Erik Gudbranson returned to the Panthers lineup after missing two games with a lower body injury. ... Hurricanes C Jeff Skinner, the team's leading scorer, missed his fourth straight game because of a concussion.