Lukas Dostal made 31 saves, then stopped two of three attempts in the shootout for the Ducks (5-3-1), who blew a two-goal lead in the third period.
Anton Lundell and Sam Reinhart scored, and Daniil Tarasov made 15 saves for the Panthers (5-5-1).
Lundell cut it to 2-1 at 11:12 of the third, lifting a shot over the shoulder of Dostal off a backhand feed from Mackie Samoskevich.
Reinhart then tied it 2-2 at 16:54 when he deflected Seth Jones’ point shot at the edge of the crease. He has scored in three straight games.
The Panthers went on the power play with 2:06 left in overtime after Mason McTavish was called for hooking, but they did not score.
Carlsson gave the Ducks a 1-0 lead at 9:59 of the second period. He and Troy Terry came through the Florida zone on an odd-man rush, and the two crisscrossed before Carlsson one-timed Terry’s pass from the right face-off circle to finish a give-and-go.
Cutter Gauthier extended it to 2-0 during a 5-on-3 power play at 12:27. He scored with a one-timer from low in the right circle off a pass from Jackson Lacombe.