Mike Matheson, a Florida defenseman, scored his first goal of the season at 2:02 of the overtime.
With Jimmy Howard down and out after making a tremendous pad save on one shot and managing to save a second by scrambling into position after the rebound, he could not stop a third shot.
Outshooting the Panthers 35-29, the Wings had many scoring chances throughout the game and could convert only one.
The Wings are now 1-5 in their last six.
Henrik Zetterberg scored his fifth goal of the season, and his first after a 22 game scoring drought, with 1:33 left in the first period.
For yet another game, the Red Wings played better than the score indicated. They had multiple chances to build a two-, three- and even four-goal lead.
From about the 13-minute mark of the first period until 8:18 of the third period, the Wings outshot the Panthers 23-9.
Tomas Tatar, Gustav Nyquist, Anthony Mantha, Dylan Larkin and others had clear scoring chances and failed to tally.
The Red Wings, challenged offensively for at least couple of seasons now, lacked "finish," once again.
Leading only 1-0, halfway through the third period, they were again victimized by a simple mistake. Nick Jensen's delay-of-game penalty at 8:22 put the Panthers on a power play and their stars capitalized.
After the Wings spent far too long in their own zone killing the penalty, Dylan Larkin finally got the puck and skated it to within a couple of feet from the blue line before two Panthers approached him, deterred him and swiped the puck.
Within moments three talented Panthers, Aleksander Barkov, Jonathan Huberdeau and Vincent Trocheck combined on Trocheck's 13th goal of the season at 10:11 of the third.
Regulation time ended 1-1, with the Red Wings outshooting the Panthers 28-14 for about the last 47 minutes.
Portions of the game were like NHL games of a different era: Danger seemed to lurk everywhere, and a penchant for violence hung in the air.
The Red Wings and Panthers collected six fighting majors in the first two periods, with the heavyweights Luke Witkowski and Micheal Haley going at it twice and Luke Glendening and Aaron Ekblad, a native of Windsor, also fighting.
Witkowski, returning from a 10-game suspension, kept the fights with Haley close.
Haley's presence on the Panthers' roster is probably what earned Witkowski the start over Tyler Bertuzzi, who is up from Grand Rapids and in need of NHL playing time and a good long look from the Red Wings.
But it was a good night to play Witkowski. The two fights were the eighth and ninth fighting majors for Haley this season, and he is making a career of fisticuffs, an unusual role in the sport in recent seasons in which fighting is generally in decline.
Glendening landed many more punches then Ekblad, including a few rights to the head in succession at the start of the fight, before eventually knocking Ekblad to the ground.
The Red Wing were skated hard by the Panthers for much of the first as Florida built a 12-6 advantage in shots on goal two-thirds of the way through the period.
Panthers forwards descended upon a defenseless Howard, at times, and controlled the puck directly in front of him in the crease without a lot of opposition.
But the Wings got some offense going, and outshot the Panthers 5-0 late in the period.
The offensive produced a goal by Zetterberg, his first in 22 games, at 18:27 of the period.
The Red Wings outshot the Panthers 12-6 in the second period, picking up their pace and time with the puck as the period went on, and beginning to dominate the game geographically.
Hotly contested, the period featured lots of combativeness in scrums and after whistles, the linesmen frequently intervening.