Patric Hornqvist ended the game in the fifth round with his first NHL shootout goal after he tied the game 3-3 with three seconds left in the third period.
"This is a huge win for us," Hornqvist said. "I think over the 65 minutes we played really good hockey, and if you keep doing that for that long of a time you know you're going to get rewarded."
On the tying goal, the Panthers kept the puck in the zone after an icing and Aaron Ekblad's shot was saved by Joonas Korpisalo. The rebound popped up and Hornqvist batted the puck into the net.
Anthony Duclair had two assists, and Sergei Bobrovsky made 19 saves for the Panthers against their former team.
Korpisalo made 28 saves for the Blue Jackets (2-2-3), who had a 2-0 first-period lead.
"Take the point and sprint out of the building. The way we played sprint, run," Columbus coach John Tortorella said. "They were the better team right from the get-go. They were the faster team. They moved the puck better. Everything about their game was better."
Florida did not begin its season until Jan. 17 after its first two games against the Dallas Stars were postponed. The Panthers also had two games against the Carolina Hurricanes postponed, all because of COVID-19 issues with their opponents.
"From start to finish we deserved that win tonight," Florida coach Joel Quenneville said. "We did a lot of great things. I liked our pace. I liked their purpose."
The Blue Jackets scored on their first two shots.
Kevin Stenlund made it 1-0 at 2:11 of the first period. Mikko Koivu, on his first shift for the Blue Jackets, passed along the right boards to Stenlund, who faked a pass then scored five-hole from deep in the circle.