Gaudreau beat Connor Hellebuyck on a nice move between the pads in the fourth round and the Flames picked up their second straight win.
Gaudreau, Andrew Mangiapane, and Christopher Tanev scored in regulation for Calgary. Jacob Markstrom, who made a couple of great saves in the shootout, turned aside 25 shots in 65 minutes. Elias Lindholm had two assists.
''I feel really comfortable,'' he said. ''Me and Sean (Monahan) are playing really good in our defensive zone. We're being smart. I don't think we've been out on the ice for a 5-on-5 goal (against),'' said Gaudreau, who is coming off his worst offensive season in 2019-20 - 58 points in 70 games.
''And we're getting our chances offensively.''
Flames head coach Geoff Ward said Gaudreau's details in his own zone and Calgary's success on the power play have been crucial to the team's early success.
''He's having fun, he's smiling coming to the rink,'' Ward said. ''When he gets time and space with the puck he can usually do good things.
''It's been a great start.''
Kyle Connor scored two power-play goals and Mark Scheifele scored for Winnipeg, which got 25 saves from Hellebuyck. Blake Wheeler added three assists.
After hitting the crossbar off the rush moments earlier, Mangiapane banged home a rebound with 6:15 left in regulation for his first of the season to give the Flames their first lead at 3-2.
But the Jets, who went up 2-0 in the first, tied things up with 1:50 remaining when Scheifele tipped Neal Pionk's point shot past Markstrom's glove for his fourth.
The game marked the first of three straight meetings between the North Division rivals at Bell MTS Place this week, with the next two set for Tuesday and Thursday.
NOTES: Gaudreau has 10 points in eight games to start the season. ... Jets center Adam Lowry saw a six-game point streak (four goals, four assists) come to an end. ... Connor scored two power-play goals in a game for the first time in his career. ... Dubois remains unavailable for Winnipeg as he continues to serve a two-week quarantine after crossing the Canada-U.S. border shortly after the deal with Columbus was finalized. The center could make his debut when Winnipeg visits Calgary Feb. 9.
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