Josh Leivo, Mark Giordano, Andrew Mangiapane and Sam Bennett scored for Calgary (16-17-3), which halted a four-game losing streak in the second of three straight games between the teams.
The series finale is Monday night in Calgary.
Gaudreau, who had two goals in nine games coming in, produced his first multi-point game in a month in his 500th career game.
''I've played for a long time with a lot of those guys in that locker room,'' Gaudreau said. ''I'm sure a lot of them are really happy for me after tonight.''
Following a 3-2 loss Friday to the Jets, Flames coach Darryl Sutter said Saturday morning: ''Hopefully he has more energy than in his 499th game.''
''I heard it,'' Gaudreau said. ''Didn't think much of it. I've been playing hockey for 24, 25 years. I know when I haven't played well and I know when I have played well.
''Personally, it's been going up and down throughout this season. Obviously, not finding the net sometimes and stuff like that. I try to work as hard as I can each night for the 23 guys in that locker room.''
Calgary is 5-5 since Sutter took over as coach on March 8.
Gaudreau played 17:05 on Saturday, second among Flames forwards behind Elias Lindholm (19:56).
''I thought his pace was better,'' Sutter said. ''Quite honestly it was his best game since I joined the team.
''He's an elite-level player in this league, so he has to try to have his best game every game for us.''
Winnipeg defenseman Logan Stanley got his first NHL goal and Mason Appleton also scored for the Jets (21-12-2), who trail Toronto by two points atop the North Division.
Playing their fourth games in six days, both clubs started their backup goalie. David Rittich made 22 saves for the win in his second start in Calgary's last 12 games.
Laurent Brossoit turned away 29 shots in the loss.
''We haven't had much puck luck at all this whole stretch,'' Sutter said. ''When you don't have a lot of pure goal scorers, you need to get that break once in awhile and we got it.''
Brossoit misplayed Bennett's shot and knocked the puck into his own net with his stick at 7:48 of the third period.
''You learn over time these guys are really proud professional athletes,'' Jets coach Paul Maurice said.
''You wouldn't say anything to anybody after a game. You'd wait, slap him in the pads the next time you're on the ice, have a chuckle about it and move on.''
NOTES: The Jets lead the 10-game season series 4-2-1. ... Winnipeg caps a seven-game road trip, its longest of the season, Monday at the Saddledome. . Flames captain Mark Giordano is one point shy of 500 for his career. . Calgary defenseman Chris Tanev got his 100th career assist. ... The 6-foot-7, 228-pound Stanley was a first-round draft pick by the Jets in 2016.
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