Bennett scored in front after taking a pass from Brad Marchand on a 2-on-1 on a play set up by Gustav Forlsing.
Bennett and Marchand each had a goal and three assists for the Panthers (13-12-2), who rallied from a three-goal deficit and never led in the game.
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 extended their point streak to five games (2-0-3). Elvis Merzlikins made 33 saves.
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 Rodrigues.
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 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 Blue Jackets lead to 4-1 at 10:24.
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 Seth 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.
Sillinger gave the Blue Jackets a 5-4 lead at 18:26 with a shot that skipped on the ice and was initially stopped by Bobrovsky but bounced off Florida defenseman Gustav Forsling and into the net.
Lundestrom made it 6-4 at 2:27 of the third period, scoring off the rush on a pass from Wood.
Marchand pulled the Panthers within a goal when he jammed in a loose puck to make it 6-5 at 4:21.
Anton Lundell tied the game at 6-6 at 14:18, scoring after Merzlikins came out to play the puck but was late getting back into position.
