Connor, who hit an empty netter with 2:49 remaining in regulation after Anaheim Head Coach Dallas Eakins elected to pull his goaltender with over four minutes remaining in the third period.
Connor then broke in on a partial breakaway, snapping a wrister past Gibson short side to seal the win for Winnipeg.
"The first one feels great," said a relieved Connor afterward.
"It's always tough … you feel a little pressure. Coming back home from a road trip, the tendency is to come out pretty slow the first period. It feels great. It's a full team effort. Helle played great back there. Special teams, we only got one power play and I thought we moved the puck pretty well," said Connor.
The win was the first of the season for road weary Jets, who kicked off their regular season with a fruitless three-game west coast swing, garnering only a single point for their efforts.
Pierre-Luc Dubois had a goal and an assist for Winnipeg.
Andrew Copp and Josh Morrissey added single goals for the Jets.
Nate Schmidt had a pair of assists.
Connor Hellebuyck made 38 saves for the Jets, who moved to 1-2-1.
Troy Terry scored the lone goal for the Ducks, who dropped to 2-3-0.
John Gibson took the loss for Anaheim, stopping 22 shots.
Troy Terry gave Anaheim an early lead with a power play marker when he redirected a Cam Fowler wrister from the point past Connor Hellebuyck to make it 1-0.
The goal was his first of the season.
The lead didn't last long as Pierre-Luc Dubois evened the contest 1:24 later when he finished off a three-way passing play after breaking into the Anaheim zone by tipping the disc past John Gibson to make it 1-1 at 4:10.
The goal was his third of the season.
Andrew Copp gave the Jets the lead just over a minute into the second when he adeptly redirected a Nate Schmidt pass just beyond Gibson's outstretched pad to make it 2-1 Winnipeg.
The goal was his third of the season.
Josh Morrissey gave Winnipeg a two-goal cushion with a power play marker early into the third period.
With Josh Manson off for tripping Morrissey one timed a Nate Schmidt feed past Gibson, beating the Ducks netminder just inside the left post to make it 3-1 Jets 1:30 into the third.
The goal was his 2nd of the season.
Kyle Connor added an empty netter with 2:49 remaining in regulation to seal the win for the Jets.
Connor scored again with 1:14 remaining, breaking in on a semi-breakaway before snapping a shot past Gibson short side to make it 5-1 Winnipeg.
The goal was his 5th of the season.
Ducks Head Coach Dallas Eakins said the loss was a learning experience for his young club.
“I think it’s a good lesson game. We had good zone time, we had good action at their net, shots-wise, things that haven’t been a real staple of our team in the past. The great lesson is; everybody now these guys they go play video games. In earlier generations we would go in the afternoon to the pool hall and play snooker. And it was always not so much what you make, but what you leave."
Winnipeg is a dangerous team. If you leave something a little too juicy they’re going to put it in your net. So I think it was a great lesson in that. We like our zone time, we like our chances at the net, we like our shot count, we like our attempts, we like the way our power play looked, but we didn’t like what we left. We have to get better at that.”
Both teams see action next on Saturday as Anaheim closes out a four-game road trip in Minnesota while Winnipeg hosts Nashville.
SHOTS-ANAHEIM 39 WINNIPEG 27
NOTES-Jets C Mark Scheifele was added to the COVID protocol list after a second positive test today.
He joins teammate Blake Wheeler, who is also in isolation after testing postive durin the latter stages of the team's recent road trip.
Both players are subject to a mandatory ten day isolation as per NHL policy.