Carter Verhaeghe scored twice and had an assist, and Seth Jones had a goal and an assist. Sergei Bobrovsky made 25 saves.
Dmitri Voronkov, Miles Wood, Cole Sillinger and Isac Lundestrom each had a goal and an assist for the Blue Jackets (13-9-6), who have lost three of five but have earned a point in each game (2-0-3). Elvis Merzlikins made 33 saves.
"Obviously when you score six goals, you give yourself a pretty good position to win," Sillinger said. "We were short for a little bit, and you don't want to give their power play any momentum. It was a high-energy game and both teams had their looks, both teams capitalized. I definitely thought we were in a good position, and the expectation is to close that game out."
Damon Severson gave Columbus a 1-0 lead at 7:40 of the first period with a power-play goal. Evan Rodrigues tied it 1-1 at 9:47, waiting out Merzlikins after Mackie Samoskevich forced a turnover at the half wall and slid the puck to him.
The teams combined for seven goals in the second period.
Voronkov gave Columbus a 2-1 lead at 5:26 after deflecting a point shot from Ivan Provorov.
Wood scored off a feed from Charlie Coyle on the rush for a 3-1 lead at 5:57.
Marchenko scored on a backhanded shot to increase the lead to 4-1 at 10:24.
"We played hard, and I think we deserved better," Provorov said. "There were a couple bad bounces and then we were short-handed quite a bit for some reason. Any time you lose, you wish you won."
The Panthers scored the next three goals to tie the game.
Verhaeghe made it 4-2 at 11:15 when he deflected a point shot from Jones.
On the ensuing power play following a failed coach's challenge by Columbus for a hand pass, Verhaeghe scored again to cut the lead to 4-3 at 13:11 off a feed from Marchand.
Jones tied the game 4-4 at 16:12 on the power play.
"It felt like you needed to win that game, just because it was right there," Florida coach Paul Maurice said. "We all felt it was right there. You can go into the room and say there are parts to your game you like, and parts you do not, but all of the pieces were part of that win."