Caleb Jones, Boris Katchouk also scored for the Blackhawks (22-37-6), who have lost six of seven (1-5-1). Petr Mrazek made 39 saves.
"They pushed, and we knew they were going to be desperate and push," Chicago coach Luke Richardson said. "They're playing for a playoff spot. I thought we persevered on the 6-on-5 and never gave up. That's been our kind of M.O. all year, and it's really good to see the guys not get discouraged. I thought we stay composed and calm and did the job to get it to overtime, and unfortunately they got the bounce, but we had our chances in overtime."
The Panthers trailed 2-0 after two periods before rallying with three goals in the third to take a 3-2 lead.
"For sure there was frustration," Tkachuk said. "Let's be real here, that's a team ranked 30th in the League. We needed the win more than they did. To be down 2-0 at any point in that game was frustrating.
"But we know they still have stuff to play for and those are tough games. It was not the start we wanted, but we did a good job in the third. We heard some boos there, but turned it around at the end and heard some cheers."
Bennett cut it to 2-1 at 8:29 of the third period, tapping in Tkachuk's pass across the goal mouth before Reinhart's power-play goal 29 seconds later tied it 2-2 at 8:58 when he tipped Tkachuk's shot from the top of the right face-off circle.
Luostarinen gave Florida a 3-2 lead at 12:42 with a shot from the high slot after taking a pass from Tkachuk.
"We were tight for two periods," Panthers coach Paul Maurice said. "There is a pressure in all of these games and we feel it every time we come to the rink. It was a must-win game, and you could feel it.
"We were not moving our feet; we were struggling to get things going. What they are good at, you saw on their first two goals. We were behind it then I think they relaxed, the pressure came off and they started to skate. These guys want to win so bad."