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.
"I liked the simplicity of the game, the shots, the tracking back, the reloads, the staying on the hunt and staying on the puck," Noesen said. "You see what we're capable of whenever we want to do that consistently throughout the whole 60 minutes."
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.
"I thought it was an up and down game," Dostal said. "I thought they really had a tight defensive zone today and we weren't able to break through but overall, I don't think our effort was bad."
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 1-1 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.
"I would have been happy had we come out of the first period with the lead, but we didn't have much offensively after [the first goal]," Anaheim coach Joel Quenneville said. "We didn't battle in the hard areas, in the trenches, around their net, and we didn't get many loose pucks or second opportunities. We didn't win our share of battles."