Ryan Nugent-Hopkins, Andrew Ference, David Perron and Taylor Hall scored in regulation as the Oilers (1-2-0) earned their first win of the season. The victory helped Edmonton avoid its worst start to a season since the 1995-96 campaign when it went 0-4 out of the gate.
New Jersey built a 3-0 lead in the first two periods before Nugent-Hopkins, making his season debut, scored after a mad scramble on a power play in front of Martin Brodeur in the Devils' net.
Nugent-Hopkins missed the first two games of the season as he recovered from shoulder surgery.
The goal spoiled Brodeur's shutout bid. There are only three teams that the veteran goalie has not recorded a shutout against in his career — Edmonton, Nashville and San Jose.
Edmonton made it 3-2 with 10-and-a-half minutes to play in the third as Ference scored on a point shot through traffic.
The momentum shifted firmly in the Oilers favour and they tied the game as Perron plucked the puck out of a face-off in the Devils end and picked the corner for his first goal as an Oiler. He came to Edmonton in an off-season trade with St. Louis.
After tying the game up 3-3 with eight minutes to play, the Oilers took their first lead of the contest two minutes later as Ales Hemsky chipped a puck off the boards to Hall, who was alone in front and slipped the puck through Brodeur's legs.
However, the Devils were able to tie the game 4-4 with just 54 seconds left while shorthanded as Elias threw a puck on net that banked off Ference's skate and into the net with Brodeur on the bench to send the game to the eventual shootout.
New Jersey scored on the game's first shot three minutes in to the first period as Jagr brought it in himself and button-hooked into the slot before sending his first of the season past Oilers goalie Jason LaBarbera.
Brunner made it 2-0 for the Devils fives minutes later on the power play. He faked a shot at the top of the circle and then elected to shoot, putting it stick-side past LaBarbera.
Edmonton's best chance in the first came with a man advantage of its own with two minutes to play when Hemsky had an open net to shoot the puck into with Brodeur going the other way, but defender Anton Volchenkov fished it to safety.
The Devils surged ahead 3-0 at the 4:34 mark of the second period as a giveaway deep in Oilers territory led to a two-on-one with Ryder electing to shoot himself, rifling his second of the season in the top corner.
Edmonton had another chance to get on the scoreboard two minutes into the third period, bur Nail Yakupov's shot rang off the post.
The Devils are right back at it on Tuesday night in Vancouver against the Canucks in the second game of a five-game trip. The Oilers are off until Thursday when they host the Montreal Canadiens.
Notes - The last time the Devils and Oilers played each other, New Jersey pulled out a 2-1 overtime win at Rexall Place on Jan. 11, 2012… Damien Brunner scored three of the New Jersey's first five goals this season… With games on back-to-back nights, Brodeur was given the start for the Devils so that off-season trade acquisition Cory Schneider could get the nod against his old team, the Canucks, on Tuesday… Nugent-Hopkins, the first overall selection in the 2011 NHL Entry Draft, made his season debut after having shoulder surgery last April… The Devils started their road trip with a completely healthy lineup… Edmonton had veteran forward Ryan Smyth sitting out as a healthy scratch, opting to inject recent call-up Ryan Hamilton into the lineup.