Calgary and Winnipeg are three points ahead of the Nashville Predators and five behind the Seattle Kraken for the first wild card. The Jets have four games remaining; the Flames have three.
Andrew Mangiapane and Nikita Zadorov each had a goal and an assist, and Jacob Markstrom made 34 saves for Calgary (37-27-15), which has won five of six.
The Flames were coming off a 4-3 loss to the Chicago Blackhawks on Tuesday.
"Still [mad] from the other night, and I think that fed into it coming into this game and a little bit more emotions than usual," said Markstrom, who started the back-to-back games. "It was a great atmosphere and a big win, but we've got to keep going here."
Duehr said, "You could say [Markstrom] won us the game, for sure. He was amazing tonight. He was huge. He bailed us out a handful of times."
Kyle Connor scored for a third straight game, and Connor Hellebuyck made 32 saves for Winnipeg (43-32-3), which was 6-for-6 on the penalty kill.
"We would have preferred to play more 5-on-5," Jets coach Rick Bowness said. "You take six penalties in a game like that, you're shooting yourself in the foot. There's no question about that. So, that's what's disappointing."