Johnny Gaudreau had a goal and two assists, and Boone Jenner, Yegor Chinakhov, Sean Kuraly and Kent Johnson also scored for the Blue Jackets (7-10-1), who are 4-1-1 in their past six games.
Matthew Tkachuk and Aaron Ekblad scored, Gustav Forsling had two assists, and Bobrovsky made 18 saves for the Panthers (9-8-2), who have lost three straight, including 5-4 in a shootout to the Calgary Flames on Saturday.
"We've got to get some people on that front [end] and score some hard ugly goals because we're having a hard time completing the plays around the net," Florida coach Paul Maurice said.
Tkachuk gave the Panthers a 1-0 lead at 7:52 of the first period, tipping in a one-timer from the left point by Forsling.
Chinakhov tied it 1-1 at 11:21 on a breakaway after intercepting a pass from Marc Staal at the Blue Jackets' blue line.
Florida outshot Columbus 18-4 in the first period.
"It's kind of been the same story all year," Panthers forward Nick Cousins said. "First period we come out and dominate the shot category and every other statistic, and after that we take the foot off the gas and the other team comes with a push.
"We've got to figure out our second period. Third periods we're fine, we come out with energy. Seconds periods have got to be better."