Jaccob Slavin and Sebastian Aho both registered a goal and assist for the Hurricanes (17-6-1). Nino Niederreiter had two assists.
Frederik Andersen made 16 saves for Carolina, which was starting a five-game road trip.
Nikolaj Ehlers and Pierre-Luc Dubois scored for the Jets (12-9-4).
Hellebuyck stopped 30 shots for Winnipeg, which ended a four-game homestand (2-2-0) at Canada Life Centre.
The Jets had a five-minute power play in the third period, but only got two shots on goal.
Carolina defenceman Ian Cole was assessed a five-minute major for kneeing and a game misconduct at 7:39 of the third after a knee-on-knee hit on Jets centre Mark Scheifele, who continued playing.
The Hurricanes led 1-0 after the first period and 3-2 following the second.
Slavin started the scoring early, registering his first goal of the season 30 seconds into the game with a point shot through traffic that went under Hellebuyck.
Carolina almost ended the period with another goal, but Hellebuyck stopped a blast from Ethan Bear with under a minute left.
The Hurricanes were all over the Jets and outshot the home team 15-5 in the opening period.
Carolina also scored early in the second period when Aho kept banging at the puck in front the net until he notched his 11th goal of the season at 1:12. A Winnipeg coach's challenge for goaltender interference was unsuccessful.
The Jets were assessed a delay of game penalty for the challenge, but Trocheck was called for hooking 33 seconds later and the play went to four-on-four. Ehlers then scored his 10th of the season with a high shot on the stick side of Andersen at 2:18.
Winnipeg had two power plays in the second period, both called on Cole for delay of game and then tripping, and the Jets made good on the second opportunity.
Blake Wheeler sent a pass to Dubois parked at the side of the net and he redirected the puck into the net with his stick between his legs at 16:06 to tie the game 2-2.
The Hurricanes ended the period with a power-play goal by Necas, who scored during a scramble in front of the net with 20 seconds remaining in the period.
Shots on goal were 30-13 for Carolina after the middle frame.
Winnipeg finished one-for-five on the power play. Carolina was two-for-three.
Jets top defenceman Neal Pionk didn't play as he was serving the first game of a two-game suspension for a knee-on-knee hit to Toronto's Rasmus Sandin in last Sunday's 6-3 Winnipeg home victory over the Leafs.
Pionk was also placed in concussion protocol and won't make the trip when the Jets head out for back-to-back games in Seattle Thursday and Vancouver on Friday. He was kneed in the head by Leafs forward Jason Spezza in the third period of Sunday's game.
The NHL handed Spezza a six-game suspension for the hit on Tuesday.
Carolina plays the Flames in Calgary on Thursday.