The shutout was Hellebuyck's fourth of the NHL season.
The win was the Jets' 8th straight against Minnesota, going back through last season.
The Jets also swept the three games this season.
Neal Pionk had a goal and an assist for the Jets.
Nikolaj Ehlers, Morgan Barron, Vladislav Namestnikov also scored for Winnipeg.
The Jets moved to 24-10-1 and have won three of their last five games.
Jesper Wallstedt turned aside 19 shots for Minnesota, who dropped to 20-10-4.
Winnipeg's power play was key in the game, going 3-5 overall and scoring after winning key faceoffs in Minnesota's end.
“It was just good execution. You see Fly’s goal, that’s just one of our multiple plays for both units off the face-offs. That was the one they called and they ran it to perfection, scoring in six seconds. And then ours, we do that play quite often with the transfer behind the net," said Pefetti, whose offensive night got in gear during the second period.
"Sometimes it’s a shot, sometimes it’s a pass, whatever it is. Neal got a hold of that one and it’s good with being sharp with execution and being sure we have a plan to just stick to that. If it works, it work, if it doesn’t, well, we can make adjustments. But tonight it worked," he said.
Nikolaj Ehlers opened the scoring 6:51 into the opening stanza just six seconds into their opening power play.
With Jon Merrill off for holding the stick, the Jets got possession off a face off win and worked the puck to Kyle Connor in the right faceoff circle.
Connor slid the disc to Ehlers, who was parked beside the crease. Ehlers slid the disc through Wallstedt's pads to make it 1-0 Jets.
The goal was his 10th of the season.
Morgan Barron made it 2-0 with just over two minutes left in the first when Alex Iafallo's shot ended up sliding through Wallstedt's pads and sat in the crease.
Barron, who was about to skate by the net, pivoted hard by the post and hammered the loose puck into the open goal.
The tally was his 3rd of the season.
Neal Pionk scored 14 seconds into a power play to put the Jets up 3-0 just over five minutes into the second period.
Jesper Wallstedt took a delay-of-game penalty when he batted the puck out of play and Winnipeg took full advantage as Cole Perfetti relayed a Nino Niederreiter pass from behind the net to Pionk, who beat the Wild goaltender with a slapshot just inside the right post.
The goal was his 5th of the season.
Cole Perfetti made it 4-0 2:07 into the third when he intercepted a break out pass from Jonas Brodin in the high slot before moving in and snapping a wrister past Wallstedt.
The goal was his 7th of the season.
Vladislav Namestnikov deflected a Neal Pionk shot past Wallstedt at 7:36 to make it 5-0 Jets.
Jets Head Coach Scott Arniel thought his club played a complete game.
“I wouldn’t say quite some time, but I would say it’s probably one of our better efforts in the last few games here. We knew they were coming in after playing last night, went after them in the first period and kind of continued that through the three periods. Liked a lot of our compete, sort of our little details. A lot of good things that happened tonight," he said.
Wild Head Coach John Hynes felt his club didn't execute their game plan and it showed.
"The mindset needs to be to play the game the right way. To play the game that gives us the best chance to win," said Hynes. "That gives us the best chance to produce offence. The best way to check, I think when you look in those areas you want to go east-west and pass up shots and play a perimeter game then you're not going to score."
Both teams see action on Monday as Winnipeg travels to Toronto while Minnesota hosts Chicago.
SHOTS-MINNESOTA 19 WINNIPEG 24
ATTENDANCE-15,225
