Frank Vatrano and Chris Kreider also scored and Lukas Dostal made 31 saves for the Ducks (7-3-1), who have won three in a row and five of six.
Jack Hughes scored and Jake Allen made 26 saves for the Devils (9-4-0), who were coming off a 4-1 win at the Los Angeles Kings on Saturday that ended a two-game losing streak.
The Ducks scored on their first shot of the game when Gauthier passed the puck ahead to Sennecke and he held off New Jersey defenseman Dennis Cholowski before lifting the puck between Allen's right arm and body from in close for a 1-0 lead at 4:13.
The Ducks nearly scored short-handed for the third straight game, but Troy Terry was stopped twice by Allen on a breakaway just past the midway point of the first period.
Anaheim made it 2-0 at 14:24 of the first when defenseman Jackson LaCombe stepped in front of Nico Hischier to intercept a clearing pass in the New Jersey zone. Referee Tom Chmielewski signaled a penalty on Hischier just as LaCombe dove forward in the slot to sweep a pass to Vatrano in the right circle, who scored with a one-timer.
Gauthier extended the lead to 3-0 at 1:54 of the first when he scored his Anaheim-leading seventh goal of the season on a sharp-angle shot from just above the goal line that slid under Allen's left pad as he protected the near post.
The Devils denied Dostal his third NHL shutout when Hughes scored his New Jersey-leading 10th goal of the season off a 2-on-1 rush to cut it to 3-1 at 7:43 of the third.
Kreider scored into an empty net with 1:54 left for the 4-1 final.
