Mackenzie Blackwood stopped 32 shots for New Jersey, who have now won two games in a row to open a five-game road trip and have registered points in six of their last seven games.
Andrew Copp scored the lone Jets goal on the night.
Connor Hellebuyck made 30 saves for Winnipeg, who lost for the first time in their last three games.
Nico Hischier scored 4:44 into the first period to give New Jersey the early lead.
Hischer shovelled a rebound past Connor Hellebuyck after Taylor Hall followed up on his own rebound.
The disc ended up right on Hischer's stick as he slid a backhand shot past Hellebucyk's outstretched pad.
Andrew Copp tied the contest 8:38 into the second when he tipped a Josh Morrissey shot from the left point past New Jersey goaltender Mackenzie Blackwood on it's way past to make it 1-1.
The goal was his second of the season.
The game took an eerie turn at 7:27 of the third period when Jets centre Bryan Little was hit by a Nikolaj Ehlers slapshot by the side of the Devils net.
The crowd waited in silence while he was tended to.
He left the ice under the assistance of a team trainer and did not return.
There was no scoring in the third period and the game went to overtime.
The play favored Winnipeg in overtime but New Jersey got a late power play when Blake Wheeler was called for tripping at 4:22.
There was no scoring in overtime and the game went to a shootout.
"They played a really hard team game out there," said Devils goaltender Mackenzie Blackwood. "It was awesome to see. Guys were buying in, blocking shots, doing self-less little plays that don't show up on the scoreboard, but affect the outcome of the game by not turning pucks over at the wrong times and managing the clock well."
The win was gratifying for the Devils, who had a rough start to the regular season, winning only twice in the month of October.
"Well you know we went through some struggles in the beginning of the year and I think there's a lot of outside noise and things like that. We really stuck to the process and we really stuck together and understood we were working through some things and it didn't seem to matter what was going on inside the locker room," said Devils Head Coach John Hynes.
"We saw our play getting better and we weren't getting the results we wanted. But it was getting better and better and that's something we talked about. Sometimes when you're in a rut you have to get your play better first. And sometimes you may play better and not win. Once you come out of it you give yourself an opportunity to win some games," said Hynes.
Though Winnipeg collected a point on the night, it wasn't the outcome the Jets wanted.
"Nothing ever comes easy for us, that’s our team," said Jets captain Blake Wheeler. "So, we gotta battle for every inch and stay in the fight, stay with it. All easier said than done, but for the most part I think our team has done that this year. There hasn’t been any give, there hasn’t been any times where we’ve – obviously, there have been times where we haven’t played out best – but for the most part it’s been us fighting through it, trying to salvage a result."
New Jersey continues their road trip on Thursday in Calgary.
Winnipeg hosts Vancouver Friday.
SHOOTOUT- NEW JERSEY-Gusev (score), Boqvist (score)
WINNIPEG-Connor (miss), Laine (miss)
SHOTS-NEW JERSEY 32 WINNIPEG 33