Finding the back of the net for the third straight game, Matthew Tkachuk put the Panthers on top early when he deftly re-directed a shot from Gustav Forsling straight over Daniil Tarasov's glove and into the top of the twine to make it 1-0 just 7:52 into the first period.
"I just knew Forsy was going to shoot it," said Tkachuk, who leads the Panthers with 25 points (eight goals, 17 assists). "I was kind of all by myself at the net. I was just able to get a piece."
Getting the Blue Jackets on the board, Yegor Chinakhov intercepted a pass at the blue line and showed off his wheels before beating Sergei Bobrovsky on a breakaway to make it 1-1 at 11:21.
On the power play early in the second period, the Blue Jackets struck again when Boone Jenner tipped a shot from Kent Johnson past Bobrovsky to suddenly make it 2-1 at 2:53.
Making it 2-2 heading into the second intermission, Aaron Ekblad took a pass from Forsling, skated toward the net and powered the puck past Tarasov to even things back up at 16:38.
On the wrong end of a bad bonce, the Panthers fell behind again when Sean Kuraly scored a shorthanded goal to give the Blue Jackets a 3-2 lead at 1:57 of the third period. Keeping their foot on the gas, Johnny Gaudreau then buried a quick short-side snipe to make it 4-2 at 7:55.
Netting his second goal of the game, Jenner scored on the power play to extend Columbus' lead to 5-2 at 18:11. Not giving up despite facing a mounting deficit, the Panthers then got one goal back and made it 5-3 when Colin White scored with 55 seconds remaining in regulation.
In defeat, Florida led 52-17 in scoring chances.
"If we were getting out-shot every night and getting out-chanced every night there'd be concern because in a hockey game you've got to drive play," Panthers head coach Paul Maurice said. "We drive lots of play here. There's another level that we can get to that's just hard to get to. We've got to get to the heavy areas."