The Jets built a 3-0 lead by the end of the first and 4-0 by the end of the second.
It was a key win for the Jets, who moved back into a Western Conference wild card playoff spot, earning their 76th point of the season.
Kyle Connor and Matthieu Perreault also scored for Winnipeg, who won their second straight.
Connor Hellebuyck made 29 saves for the Jets.
Marc-Andre Fleury turned aside 20 shots for the Golden Knights, who dropped to 37-24-8.
Winnipeg didn't wait to get their offensive game on track as Nikolaj Ehlers got the Jets on the board 32 seconds into the contest when the Jet winger broke wide around the Golden Knights goal, leaving defenceman Zach Whitecloud in his wake before centering the puck.
The disc careened off of Vegas forward Ryan Reaves' stick before goaltender Marc-Andre Fleury kicked it into his own goal.
The goal was his 24th of the season.
Winnipeg took a 2-0 lead on the power play at 4:41 when Patrik Laine blasted a shot past Marc-Andre Fleury at 4:41.
With Nick Cousins off for tripping Neal Pionk's shot from the point was blocked by Golden Knights defenceman Brayden McNabb but the puck careened right to a waiting Laine who stopped the puck with his backhand before beating Fleury just inside the left post with a low shot.
The goal was his 27th of the season.
Kyle Connor made it 3-0 at 18:10, coverting a Jack Roslovic feed.
Vegas forward Nicolas Roy put the puck right on his tape just inside the Jets blue line before the Jet centre broke up ice with it before hitting Connor with a crisp pass which he promptly buried to score his 36th goal of the season.
Matthieu Perreault made it 4-0 with a power play marker after Josh Morrissey hit him with a hard pass as he was cutting through the slot.
The Jet winger flipped the puck past Fleury, beating him glove side to score his 7th goal of the season with six minutes remaining in the second.
There was no scoring in the third period.
SHOTS-VEGAS 24 WINNIPEG 29