Blake Wheeler and Mark Stuart also scored for the Jets (4-4-1).
Jonathan Huberdeau and Tomas Fleischmann scored for the Panthers (3-6-0).
The Jets came out flat in the first, giving away the puck four times and winning only one of 10 faceoffs.
They came up short on their lone power-play opportunity in the first, when Tobias Enstrom cut their two minutes down to one with a hooking call.
On their best scoring opportunity, Bryan Little's shot went high and, even though it bobbled up and around the net, linemate Andrew Ladd couldn't get control of the puck for a follow-up.
Huberdeau banged in Drew Shore's rebound at 18:12 to make it 1-0 just before the end of the first. The Panthers outshot the Jets 7-3 and Winnipeg didn't get credited with a shot until almost 14 minutes had passed.
They came on stronger in the second and Wheeler put the Jets on the board from the point at 2:28 when he slammed a pass from Enstrom past Florida netminder Scott Clemmensen.
But Florida took the lead back less than two minutes later on Fleischmann's mirror-image shot from the point that sailed past Ondrej Pavelec.
Stuart's wrister, his first goal this season, sailed between Clemmensen's pads at 12:21 to tie it again, as the Jets outshot Florida 14-5 in the period.
The third was scoreless and neither team could capitalize on a power-play opportunity but the Jets finally made the extra man work with 16 seconds left in overtime.
Notes: The Jets started the game with the highest-scoring defence in the NHL — seven goals and 26 points — led by Enstrom's team-high 11 points. ... The Panthers' Peter Mueller had scored a goal in each of his last four games.