The Jets scored twice in the game's first three minutes to get the lead.
Gabriel Vilardi, Brad Lambert, Vladislav Namestnikov scored the other Jet goals.
Eric Comrie turned aside 28 shots for Winnipeg, who moved to 9-3-0.
Sidney Crosby and Eric Lizotte scored for the Eastern Conference leading Penguins.
Arturs Silovs made 29 saves for Pittsburgh, who dropped to 8-3-2.
Gabriel Vilardi gave Winnipeg the lead 15 seconds into the contest after he picked up a rebound off a Josh Morrissey point shot before moving behind the Penguin goal and banked the disc off of Silovs' skate.
The goal was his 5th of the season.
Brad Lambert made it 2-0 just under two minutes later when Parker Ford gained control of the puck in the neutral and drove the net hard on his backhand before throwing the puck across the crease.
Lambert stuffed the loose puck past Silov's pad to score his first NHL career goal.
Vladislav Namestnikov converted a Jonathan Toews feed 1:17 into the second period to give Winnipeg a 3-0 lead.
Toews took control of the puck by the Jet blue line before curling hard and gaining the offensive zone before hitting Namestnikov's stick with a hard pass he simply redirected into the net.
The goal was his 6th of the season.
Kyle Connor scored on a shorthanded penalty shot 12:13 into the second after Penguins goaltender Arturs Silovs tripped him by throwing his goalstick when the Jet winger was about to score into an empty net.
The goal was his 7th of the season.
With Neal Pionk off for holding, Sidney Crosby got the Penguins on the board 25 seconds into the power play when an Erik Karlsson blast from the point went in off of his body at 19:48.
The goal was his 9th of the season.
Eric Lizotte was credited with a goal 10:27 into the third after Jets goaltender Eric Comrie knocked a loose puck into his own goal.
Kyle Connor added an empty netter with 1:21 remaining in the third period to clinch the win for the Jets.
Winnipeg begins a six-game road trip on Tuesday against Los Angeles while Pittsburgh wraps up a four-game road trip on Monday in Toronto.
SHOTS-PITTSBURGH 30 WINNIPEG 34
ATTENDANCE-14,262
