It had been 12 years since Anaheim had last won on New Jersey's home ice.
The Ducks captured their third straight and improved to 3-4 on a nine-game road trip. Jonas Hiller picked up the win with 34 saves.
The Devils missed out on a chance to move past idle Philadelphia and Pittsburgh into first place in the Atlantic Division.
Both of Carter's goals came in the opening period. He beat Brodeur with a slap shot with 9:48 remaining. He tallied again with 2:07 to go in the frame.
Swim Week Miami Beach 2014 [PHOTOS]