Beckett Sennecke had a goal and an assist, and Chris Kreider had two assists for the Ducks (34-24-3), who were coming off a 5-1 loss to the Colorado Avalanche on Tuesday that ended a five-game winning streak.
Anders Lee scored, and David Rittich made 21 saves for the Islanders (35-22-5), whose five-game winning streak ended in the opener of a four-game road trip.
Anaheim gave up the first goal for the fifth straight game when Lee scored on a rebound after Husso had saved his tip attempt, giving New York a 1-0 lead at 4:58 of the first period.
The Ducks were on a power play when Sennecke made a pass from behind the Islanders net to Gauthier in the left face-off circle and he scored with a one-timer to the far side to tie it 1-1 at 12:56.
Gauthier then gave the Ducks a 2-1 lead at 16:05. He scored his Anaheim-leading 31st goal of the season with a one-timer from the right circle off a feed from Leo Carlsson, giving him five goals in the past three games.
Anaheim extended the lead to 3-1 at 18:40 when Sennecke one-timed a rebound from the left side for his 20th goal of the season.
Ryan Poehling pushed it to 4-1 at 2:11 of the third period, sliding the puck over the goal line with a backhand from in close, before Frank Vatrano scored into an empty net with 4:11 remaining for the 5-1 final.
