The victory was the fourth straight for the Devils, marking the first time they have won at least that many in a row since Jan. 7-16, 2023, when they won five in a row.
Jesper Bratt had a goal and an assist, Nico Hischier had two assists, and Jake Allen made 27 saves for the Devils (4-1-0). Connor Brown scored in his first game against his former team since signing a free agent contract with New Jersey on July 1.
Ryan Nugent-Hopkins scored two goals, Connor McDavid had two assists, and Calvin Pickard made 18 saves for the Oilers (2-2-1), who have lost two straight.
Hughes gave New Jersey a 1-0 lead at 8:07 of the second period. After getting a pass from Brett Pesce in stride near the Oilers blue line, he skated past three Edmonton players in the high slot before scoring on a wrist inside the far post from the left face-off circle.
Bratt pushed it to 2-0 with a power-play goal at 16:02, scoring on a backhand from low in the right circle.
Nugent-Hopkins pulled the Oilers within 2-1 just 2:14 later on a snap shot from below the left circle at 18:16.
Brown then scored on a short-handed breakaway for a 3-1 lead at 10:37 of the third period, putting a wrist shot over the glove of Pickard.
Hughes made it 4-1 at 12:33 when he skated into the slot and went backhand to forehand following an Edmonton turnover.
Nugent-Hopkins cut it to 4-2 at 16:30 with his second of the game. He scored from in front off a McDavid pass with Pickard pulled for an extra attacker.
Dawson Mercer scored an empty-net goal to give New Jersey a 5-2 lead at 18:53.
Curtis Lazar, who signed a free agent contract with the Oilers on July 2 after three seasons with the Devils, scored from the top of the slot at 19:57 for the 5-3 final.