The win was Winnipeg's fourth straight.
Earlier in the day, Hellebuyck spoke to the media for the first time since losing in the playoffs last spring.
The Devils announced earlier that Hellebuyck was not going to be facing his old team and he spent the night out of sight of the Winnipeg fans watching from the dressing room.
Cole Perfetti had a pair of assists for the Jets.
Nico Daws stopped 19 shots for Winnipeg, who Jasper Bratt, Cody Glass scored for the Devils.
Jake Allen turned aside 21 shots for New Jersey, who saw their five-game winning streak snapped.
Dawson Mercer opened the scoring 7:54 into the first when he turned and fired the puck at the net from forty feet out past a screened Jake Allen to give the Jets a 1-0 lead.
Kyle Connor scored on the power play at 15:06.
With the Jets enjoying a two-man advantage Connor's attempted centering pass went in off of Devil defenceman Brenden Dillon's skate.
The goal was his 14th of the season.
Jesper Bratt cut the Jet lead in half early into the second period when he one timed a centering pass from Arseny Gritsyuk past Daws, ringing the shot in off the inside of the right goalpost.
The goal was his 4th of the season.
New Jersey tied 44 seconds later when Cody Glass tipped a Jonathan Kovacevic shot past Daws to make it 2-2.
Mercer put the Jets ahead on the power play at 11:58 when he finished off a neat three-way passing play, firing the puck into a wide open net to make it 3-2.
The goal was his 3rd of the season.
Kyle Connor added an empty netter to seal the win for the Jets.
SHOTS-NEW JERSEY 21 WINNIPEG 25
ATTENDANCE-15,209
