Connor Brown had a goal and an assist for the Devils (10-5-0), who are 6-1-0 in their past seven games. Connor Hellebuyck made 18 saves for his third straight win in his first start at Prudential Center as a member of the Devils. The 33-year-old goalie was acquired in a trade with the Winnipeg Jets on Oct. 23.
Evan Bouchard and Ryan Nugent-Hopkins, who became Edmonton's all-time leader in games played (1,038) on Tuesday, each had a goal and an assist for the Oilers (11-2-3). Kasperi Kapanen had two assists and Tristan Jarry made 31 saves for Edmonton, which lost for the first time in eight games on the road this season (7-0-1), but does have points in its past five games (3-0-2).
Connor McDavid had one assist to extend his season-opening point/assist streak to 16 games. The Oilers captain leads the NHL with 31 assists.
Arseny Gritsyuk scored in the top of the fourth round of the shootout and Hellebuyck stopped Kapanen to secure the victory.
Bouchard gave the Oilers a 1-0 lead at 8:29 of the first period on a slap shot from the top of the left face-off circle to extend his point streak to four games.
Brown tied the game 1-1 with a power-play goal at the left post at 7:42 of the second period, chipping in the loose puck on the rebound of his netfront redirect of a Hughes shot.
Hughes scored twice in a span of 45 seconds for a 3-1 lead.
He connected on a one-timer from the right face-off circle at 14:50 of the second for a 2-1 lead and then scored on a backdoor play at the left post at 15:35, the puck going in off his left skate from a cross-crease pass from Brown.
Nugent-Hopkins pulled the Oilers within 3-2 with a power-play goal on a shot from the top of the left face-off circle that deflected off the stick of Brown at 18:16 of the second.
Leon Draisaitl made it 3-3 on a one-timer from the right circle during a 5-on-3 power play 1:00 into the third period. McDavid earned the second assist on the play to keep his NHL-record season-opening assist streak alive.