Zach Parise scored a power play goal 66 1, on Wednesday night.
Patrik Elias set up the game-winner with a pass from the side of the net that found Parise in front of the crease. Corey Potter was off for Edmonton after taking a tripping penalty with 36 seconds left in the third period.
Ilya Kovalchuk scored the other goal on a shorthanded break and had two points for the Devils, who won for the third time in four games. They are 11-2 in overtime this season.
Ales Hemsky tied the game 8:32 into the third period, making it 1-1 with a slap shot from the left side that got through a screen.
But the Oilers fell to 4-14-2 in their last 20 games and couldn't rebound from a 1-6 road trip. They earned a point for only the third time in their last 13 games.
"We came back from 1-0 in the third. It's not like we had a 3-1 lead and gave it up," said Edmonton's Taylor Hall, who had an assist. "When you're losing going into the third and you come out with a point, it's not always a bad thing."
The Devils broke a scoreless tie suddenly.
They were shorthanded on David Clarkson's interference penalty, but Kovalchuk cheated to steal a pass at the blue line and skated directly at Khabibulin on a breakaway, snapping a low shot that beat the goaltender into the right side of the net.
It was New Jersey's league-high 11th shorthanded goal this season.
Parise extended his point streak to five games (two goals, six assists) and Kovalchuk upped his to four games (5g, 3a)...The Devils are 2-1 on a four-game road trip.