Defenseman Sami Vatanen appeared to score 16 seconds into his first game in Anaheim since the Ducks traded him to the Devils on Nov. 30, but he was ruled offside after beating goalie John Gibson (15 saves) with a slap shot.
New Jersey goalie Keith Kinkaid, who started for the second straight game after making 38 saves in a 3-0 win at Los Angeles on Saturday, made 32 saves.
Getzlaf scored into an open net for a 1-0 lead at 1:14 when Kinkaid found himself out of his crease after making a difficult save on a Rakell redirection from in close.
The Ducks were outshooting the Devils 11-2 when Silfverberg made it 2-0 at 6:37 of the first period.
"We had a great start," Anaheim coach Randy Carlyle said. "We had to have a good start. That's paramount to getting things going for us in our building. They played yesterday afternoon, so you try to take advantage of that as much as possible."
The Ducks committed two minor penalties 17 seconds apart in the final minute of the first period, and the Devils had a 5-on-3 for 1:25 to start the second but were unable to capitalize.
Palmieri, who was selected by the Ducks in the first round (No. 26) of the 2009 NHL Draft, scored his 20th goal, on the power play, at 10:31 of the second period to cut the Anaheim lead to 2-1.
Montour made it 3-1 with a power-play goal at 7:55 of the third period.
Maroon, who played for Anaheim from 2011-16, got the Devils to within 3-2 at 10:05, but Rakell deflected a point shot from defenseman Cam Fowler at 10:51 to make it 4-2.
"We didn't get negative after they scored," Rakell said. "We kept coming after them."
