Gauthier joined Corey Perry (2010-11 and 2014-15), Frank Vatrano (2023-24) and Teemu Selanne (1997-98) as the only Anaheim players to record three hat tricks in a single season.
Gauthier also had an assist, Mikael Granlund had a goal and three assists, and Jackson LaCombe also had three assists to stretch his assist streak to 10 games (15 assists) for the Ducks (10-7-1), who have won five in a row. Laurent Brossoit made 32 saves.
Kris Letang and Rickard Rakell scored, and Evgeni Malkin had two assists for the Penguins (6-10-2), who were coming off a 5-2 win at the Los Angeles Kings on Saturday that ended a four-game losing streak (0-3-1). Arturs Silovs made 20 saves.
Anaheim scored just as its first power play expired when Declan Carlile blocked a shot by Gauthier and the puck went into the slot, where Granlund fired it into the net for a 1-0 lead at 8:26 of the first.
LaCombe assisted on the goal to tie Ryan Getzlaf and Perry (both 10 games in 2009-10) for the longest assist streaks in team history.
Gauthier put a no-look shot between Silovs' pads from the right face-off circle to stretch the lead to 2-0 at 6:28 of the second period and give the Ducks a power-play goal in eight straight games.
Gauthier scored with a wrist shot from the slot to make it 3-0 at 9:11.
Anaheim scored again on a power play when Tristan Luneau hit the net with a point shot to push the lead to 4-0 at 5:12 of the third.
Letang scored after Pittsburgh went on a power play at 6:40 of the third and pulled Silovs for a 6-on-4, cutting the lead to 4-1 at 8:05.
Rakell followed with another 6-on-4 power-play goal to bring the Penguins to within 4-2 at 13:42.
Gauthier scored into an empty net to complete the hat trick at 19:26 for the 5-2 final and the 13th goal of his goal streak.