Miles Wood had two goals and an assist for New Jersey (8-3-0), which has won five straight (outscored opponents 23-8).
"That was a huge win for us. They were 7-3 just like us heading into this game," Wood said. "They're a great team, and to come back like that in the third period was a great sign, and it was a big win for us. It was huge to come back like that in the third. It just showed a huge sign of strength by all the guys on the team."
Mackenzie Blackwood allowed two goals on 18 shots before leaving in the second period with an undisclosed injury. Vitek Vanecek made 18 saves in relief.
Connor McDavid had a goal and assist, Tyson Barrie had two assists, and Skinner made 39 saves for the Oilers (7-4-0), who had a five-game winning streak end.
"I definitely feel we should have won," McDavid said. "I definitely feel like we created enough chances. We probably gave up too many chances, but I thought [Skinner] gave us a great chance to win. You have a team on the ropes, and we had a couple looks there, and you've got to put them down. You have to find a way to close that one out."
McDavid scored his 12th of the season to give Edmonton a 1-0 lead at 9:20 of the first period, finishing a pass from Zach Hyman on a 2-on-1.