Reid Boucher set up a goal and scored the game-winner 7:13 into the third period, and the Devils edged the Oilers 2-1 after retiring Martin Brodeur's jersey in a rousing ceremony Tuesday night.
Adam Henrique also had a goal and an assist as the Devils snapped a three-game losing streak and sent the Oilers to their third straight loss.
Cory Schneider made 19 saves for New Jersey, including 1-on-1 stops in the first period against Taylor Hall and Connor McDavid. Schneider also denied Leon Draisaitl in close in the final minute.
McDavid, the top pick in last year's draft, set up Jordan Eberle's goal for Edmonton. Cam Talbot made 24 saves.