Fleischmann's second goal was an empty netter with 41 seconds left in regulation that seemed to ice the game at 3-1, but Montreal's Erik Cole raced down the right side of the ice after the Canadiens won the ensuing faceoff and slipped a backhander past Scott Clemmensen 11 seconds later to bring Montreal back within a goal.
The Canadiens could not net the equalizer, though, despite firing a flurry of shots at the net in the closing seconds as Florida hung on for the win.
Shawn Matthias scored the other goal for the Panthers, winners of two of their past three games.
Jose Theodore started in net for Florida and stopped 9-of-10 shots, but left the game in the second period with a lower body injury. Clemmensen entered in relief and allowed one goal on 18 shots.
Travis Moen and Cole scored for Montreal, which dropped its seventh game in its last eight tries.
Carey Price stopped 32-of-34 shots in defeat.