Jaccob Slavin and Sebastian Aho each had a goal and an assist for the Hurricanes. Nino Niederreiter had two assists. Frederik Andersen made 16 saves for Carolina, in the opener of a five-game road trip.
The Jets had a five-minute power play in the third period and managed only two shots on goal.
Head coach Rod Brind'Amour was impressed with his team's penalty kill.
"That could have been real crucial," Brind'Amour said. "If (the Jets) get one, they get momentum, who knows what happens?
"We didn't give them anything. Like I said, that was one of the big keys of the game, for sure."
Carolina defenseman 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 center Mark Scheifele, who continued playing.
Nikolaj Ehlers and Pierre-Luc Dubois scored for the Jets. Connor Hellebuyck stopped 30 shots as Winnipeg wrapped up a four-game homestand (2-2-0).
"I think maybe a little bit more support to the guy that has the puck is something that we should have changed a little," Ehlers said.
"We did score a power-play goal today, but obviously when you're behind 4-2 and you get a five-minute power play, you want to at least get some momentum going. And we weren't able to do that. We'll be better next game."
The Hurricanes led 1-0 after the first period and 3-2 after the second.
"We just weren't prepared to play. That's my job," Jets head coach Paul Maurice said. "For the style of game that was going to be played today, we didn't skate nearly well enough to expect to win."
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 outshot the Jets 15-5.
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 Anderson's stick side at 2:18.
Winnipeg had two power plays in the second period, both called on Cole for delay of game and tripping, and the Jets made good on the second opportunity.
Blake Wheeler sent a pass to Dubois parked at the side of the goal and he redirected the puck into the net with his stick between his legs at 16:06 to tie the game at 2-all.
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.
Carolina had a 30-13 edge in shots after the middle frame.
Winnipeg finished 1 for 5 on the power play. Carolina was 2 for 3.
"Penalty kill is something that we take pride in as a group ..., " Slavin said. "You step over those boards and you've got a job to do and everyone was up for the task tonight. That five-minute kill, it's huge."
Jets top defenseman Neal Pionk didn't play. He was serving the first game of a two-game suspension for a knee-on-knee hit to Toronto's Rasmus Sandin in Sunday's 6-3 victory over the Toronto Maple Leafs.
Pionk was also placed in concussion protocol. 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.
Hurricanes: At Calgary Flames on Thursday in the second game of a five-game trip.
Jets: At Seattle Kraken on Thursday in the opener of a back-to-back. At Vancouver on Friday.