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.
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.