Stefan Noesen had a goal and an assist, and Ondrej Palat and Juho Lammikko each had two assists for the Devils (18-13-1), who have won two of their past three games.
It was the first home win for the Devils since a 3-2 overtime victory against the St. Louis Blues on Nov. 26.
Troy Terry scored, and Lukas Dostal made 18 saves in his return after missing nine games with an upper-body injury for the Ducks (19-12-1), who have lost two straight games after winning three in a row.
Terry gave the Ducks a 1-0 lead on a snap shot from the right hashmarks after taking a lead pass by Leo Carlsson at 13:18 of the first period.
Noesen tied the game on a shot from the slot at 16:09 of the first. Lammikko skated hard down his right wing before backhanding a pass to Noesen from behind the goal line.
Paul Cotter gave the Devils a 2-1 lead on a wrist shot in the slot at 5:52 of the second period.
Cody Glass pushed it to 3-1 at 17:04 of the second on a snap shot from the high slot.
Allen made 14 saves in the third period, including a pad stop against rookie Beckett Sennecke at 16:07 on a backhand from the slot with Dostal pulled for a 6-on-5 advantage.
Connor Brown scored an empty-net goal at 18:00 of the third for the 4-1 final.
Forward Arseny Gritsyuk (upper body) and defenseman Simon Nemec (lower body) did not play for the Devils, who also remained without forwards, Jack Hughes (finger), Zack MacEwen (lower body), Evgenii Dadonov (wrist) and Timo Meier (personal leave), and defensemen Brett Pesce (hand) and Jonathan Kovacevic (knee).