After Andrei Vasilevskiy made the save against MacKenzie Weegar, Hedman beat Florida forward Jonathan Huberdeau down the ice, took a pass from Alex Killorn just outside the Panthers blue line, and went in alone against goalie Chris Driedger.
"The puck bounced our way, and I was able to join the rush," Hedman said. "[Killorn] made a nice play and passed it at the right time to give me a breakaway. I tried to have some patience on the breakaway, and I was able to find the back of the net."
Ross Colton tied the game in the third period for the Lightning (29-12-2), who won for the third time in six games. Vasilevskiy made 36 saves to improve to 14-0-0 at home.
"You're down 2-1 in a big-time game with two pretty good hockey teams, and you find a way to tie it and find a way to win it in overtime," Tampa Bay coach Jon Cooper said. "The boys dug their heels in and pulled one out."
The Lightning are tied for first place with the Carolina Hurricanes in the eight-team Discover Central Division, one point ahead of the Panthers, who lead the fourth-place Nashville Predators by 10 points. The top four teams will qualify for the Stanley Cup Playoffs.
Patric Hornqvist and Anthony Duclair scored, and Markus Nutivaara had two assists for the Panthers (27-12-5), who have lost four of five. Driedger made 16 saves.
The teams will play again here Saturday.
"I looked at the schedule, and we play them [three more times] heading into the playoffs," said defenseman Brandon Montour, who was plus-2 with one hit and one blocked shot in 17:59 in his Florida debut. "Whether we play them in the playoffs or not, we have got to get through them, or they've got to get through us. We have to keep building off each game until the playoffs come, and you never know what could happen there."
Colton scored from the left of the net on a redirection of a pass from Mikhail Sergachev from the slot to tie it 2-2 with 10:03 remaining.
"That [goal] was huge, especially with the way things are going," Hedman said. "When you go down 2-1, it's easy to fall back into that. Ross has been a difference maker ever since he's been called up (from Syracuse of the American Hockey League on Feb. 15). He competes hard every night."