They came up with a late barrage of goals to end their long losing streak.
``If you know ... they are tired, you've got to keep on going after them, make sure they make a mistake,'' said Fleischmann, the beneficiary of a late miscue. ``They did, and that's why we won the game.''
Jacob Markstrom stopped 33 shots while flirting with his first career shutout, and Filip Kuba had two assists for the last-place Panthers, who scored the first three goals and held on to snap their six-game slide.
Markstrom was 2:33 from the shutout when Jordan Staal scored on the power play for Carolina.
``Our effort and our compete was there. I thought we looked a little worn-down but we were staying with our structure and our system,'' captain Eric Staal said. ``It was a 0-0 game going into the third period, and some mental mistakes and it ends up in the back of your net.''
An untimely turnover by Bobby Sanguinetti - one of three Carolina defensemen who were injured in the first two periods - wound up turning into the game's first goal.
His misplay near Ellis sent the puck to Tomas Kopecky, who set up Fleischmann's wrister to make it 1-0 at 7:39.
``We could tell they were getting tired, minute by minute, and our forechecking, that's what got us the first goal,'' Fleischmann said. ``And then we just, I would say, played better than them and better physically.''
Goc scored on a tip-in on a 5-on-3 power play at 12:47, and Matthias - who was ill with flu-like symptoms, slept all day and was a candidate to be scratched - added a goal with the man advantage at 13:51.
``I don't want to miss any games,'' Matthias said. ``I want to play and get us out of this.''
Jerred Smithson added an empty-netter with 52.4 seconds left.
That was plenty of offense for the Panthers behind Markstrom, the second-year goalie who entered 1-5-1 this season with a goals-against average of 3.29.
He certainly found a groove against a Carolina offense that, until the final minutes, had sputtered. Since blowing a 2-0 lead in a 3-2 loss to division rival Washington on March 14, the Hurricanes have managed just three goals in their next three games.
Their power-play unit, the second-worst in the NHL, struggled against the Panthers' league-worst penalty-kill, missing their first three chances before Jordan Staal's late goal - Carolina's first with the man advantage since March 9.
Their frustration boiled over when Alexander Semin skated to the bench after his shift ended and whacked his stick on the boards.
``I thought actually at times tonight, it actually looked better than it has in a month,'' coach Kirk Muller said. ``There's just no results. You've just got to let them sort through it and get one goal, and I think their confidence level will grow on it and then it'll just come natural again.''
Semin's frustration came during a critical 4-minute power play after Scottie Upshaw received a double-minor for high-sticking a bloodied Tim Gleason - one of those three injured Hurricanes defensemen.
Justin Faulk suffered an apparent right leg injury during a collision behind the boards with Jack Skille moments before Gleason was hurt and didn't return, while Sanguinetti appeared to take a skate to his face with 7:03 left in the first but was back for the second. Gleason returned for the final 2 minutes of the period.
Muller said Faulk would be evaluated Wednesday.
``When we lost Faulk, more than anything, going to five (defensemen), back-to-back games, really hurt our D going into that going into the third,'' Muller said. ``It kind of starts to put some holes in the game going into the third period.''
Both teams certainly had plenty of chances early: Semin clicked a pass off the shaft of a Florida player's stick on its way across the crease, Kevin Westgarth rang the post, and Drayson Bowman had a breakaway yet couldn't get a shot off on Markstrom after the puck rolled off his stick.
The Panthers - who won for just the seventh time since beating Carolina in the opener - couldn't get anything past Ellis for two periods, either, despite peppering him with a handful shots in roughly a minute of the first.
Notes: The teams split the season series 2-2. ... Carolina's record against the Panthers at PNC Arena is 28-7-4. ... Westgarth dropped LW Eric Selleck during a brief fight with 2:58 left. Selleck received an instigator misconduct. ... Before the game, the Panthers recalled C Quinton Howden from San Antonio of the AHL, then scratched him.
Follow Joedy McCreary on Twitter at (at)JoedyAP.