Chad Johnson made 25 saves for the Flames (22-19-2).
"They seemed to just have a little extra out there, I don't know what it was," Johnson said. "They came pretty hard at us, got pucks deep. They used that momentum there and they just had a little extra, a little more want at the end of the night.
"They played really good defensively. It was hard to get good looks on shots on Hellebuyck, and when we did have anything, he was making the save. I just thought they played harder, and that's pretty much all it came down to."
Byfuglien scored his sixth of the season to make it 1-0 at 10:21 of the first period. He took the puck at the Flames blue line, rushed around defenseman Mark Giordano, toe-dragged the puck to his forehand, and shot over Johnson's glove hand.
Wheeler made it 2-0 at 3:16 of the second after causing defenseman TJ Brodie to turn over the puck at the Flames blue line. Wheeler beat Brodie to the loose puck and shot to the short side over Johnson's glove for his 12th of the season.
"It's frustrating. Definitely not what I planned on happening," Brodie said. "But at the end of the day, it's over with. The more you think about it, the more it affects you. It's time to move on."
Jets left wing Nikolaj Ehlers and Flames left wing Johnny Gaudreau each had a breakaway in the second period. Johnson was able to get his stick down to cover the five-hole to stop Ehlers at 9:37, and Hellebuyck's poke-check got enough of Gaudreau's stick, sending the puck into the corner and out of harm's way with 45 seconds remaining.