Nate Thompson, Andrew Copp and Pierre-Luc Dubois also scored for Winnipeg. Nikolaj Ehlers had three assists and Kyle Connor added two. Connor Hellebuyck made 29 saves for the win.
After a 4-2 loss to the Flames on Saturday, Jets coach Paul Maurice shuffled his lines, putting Scheifele, Connor and Ehlers together. They combined for eight points.
''You've got two skilled fast guys like Nik and K.C., you've got to keep your speed going,'' Scheifele said. ''Let them get going and get roaming around in the offensive zone.''
Scheifele switched places with Dubois, who scored on a line with Paul Stastny and Blake Wheeler.
''When you play with Wheels and Stas, they're both such smart players,'' Scheifele said. ''You just make the simple plays over and over and over and that's how we get success. Two very different lines, but obviously four very talented players that you're playing with. It's fun no matter who you're playing with on this team.''
Maurice also wanted to see how his new trio would play.
''Those three guys will work really well together in certain matchups I think,'' Maurice said. ''What we need to do in the last 20 games is get two or three options depending on the kind of teams we're playing.''
Winnipeg leads the nine-game season series against Calgary 5-2-1. After three meetings in four days, the teams don't face each other again until May 5.
Elias Lindholm scored for Calgary. Jacob Markstrom stopped 19 shots over two periods and David Rittich had five saves on six shots in the third.
Winnipeg remained second in the North Division and a point behind the front-running Toronto Maple Leafs.
The Flames trailed the fourth-place Montreal Canadiens, who held down the final playoff berth, by two points.
''It's been win one lose one, win one lose won, win one lose three,'' Calgary forward Matthew Tkachuk said. ''Time is ticking. We've been saying this for the past however long, but time is really ticking. If we have any hope or chance of stringing a bunch together against all these teams ahead of us, we have to dig down deep. I certainly have to be a hell of a lot better than I was tonight.''
Scheifele scored his second of the game at 3:31 of the second to push the Jets' lead to 3-1. Ehlers skated the puck deep and dished to Scheifele, who top-shelfed his own rebound.
Officials disallowed a Flames goal at 5:32 ruling that Milan Lucic interfered with Hellebuyck on the play.
Copp put Winnipeg up by three with 5:29 left in the second as he redirected Ehlers' cross-ice setup past Markstrom's right toe.
Dubois scored on a rising wrist shot from the top of the circle at 1:04 of the third period. It was the second shot Rittich faced in the game.
A tic-tac-toe passing play below the hashmarks with Johnny Gaudreau and Tkachuk opened the net for Lindholm's power-play goal 2:24 into the game.
Winnipeg took the lead with two goals in less than two minutes late in the first.
Thompson tied it with 3:41 left. The play was reviewed to determine if he'd kicked Dylan DeMelo's shot on goal into the net but it stood. Schiefele's one-timer off the rush on Connor's pass beat Markstrom stick-side with 1:47 to go in the period.
Connor has a goal and four assists in his last three games
Flames F Josh Leivo played in his 200th career game.
Winnipeg has used the same 18 skaters and two goalies in 11 straight games.
Jets: Host Toronto on Wednesday night to open a four-game homestand.
Flames: At Vancouver on Wednesday night to open a two-game trip.
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