Gauthier also had an assist for his first career four-point game.
Nikita Nesterenko had a goal and an assist, and Leo Carlsson and Troy Terry each had two assists for the Ducks (8-3-1), who have won six of seven. Lukas Dostal made 18 saves.
Evan Rodrigues had a goal and an assist, and Brad Marchand and Eetu Luostarinen also scored for the Panthers (6-6-1), who were 2-0-1 in their previous three games. Sergei Bobrovsky made 25 saves.
Gauthier gave Anaheim a 1-0 lead at 3:09 of the first period, scoring five-hole on a breakaway.
Marchand tied it 1-1 at 10:14 on a breakaway following a Ducks turnover in the neutral zone.
Gauthier scored on the power play to put the Ducks back ahead 2-1 at 15:17 with a one-timer from the right circle.
Rodrigues scored on a breakaway to tie it 2-2 at 5:21 of the second period before Luostarinen’s power-play goal gave Florida a 3-2 lead at 10:37. He scored from in close off a feed from Rodrigues.
Anaheim then scored five consecutive goals.
Gauthier scored again on the power play to complete the hat trick and tie it 3-3 at 15:36 with a one-timer from the right circle. It was his Ducks-leading 10th goal of the season.
Nesterenko moved Anaheim in front 4-3 at 17:19 of the second when he scored his first goal of the season on a rebound.
Rodrigues went to the locker room after a collision with Carlsson on a power play 51 seconds into the third period, resulting in a five-minute major interference penalty and a game misconduct on Carlsson.
Rodrigues returned just before Jacob Trouba scored a rebound to extend it to 5-3 at 11:43 of the third period.
Chris Kreider scored off a tip to push it to 6-3 at 13:21, and Jansen Harkins swept the puck into the net while on his stomach at 14:47 for the 7-3 final.
