Jack Roslovic scored for Winnipeg (31-16-2), which has lost two in a row. Laurent Brossoit made 28 saves.
"I thought we outplayed them, for the most part," Brossoit said. "The goalie on the other end had a good game, lot of key saves, especially on the power play in the first period. That got them into the game, and he was hot from then on in. And they did a good job in the third period sitting on the lead."
Hart was strong early, including four saves at the end of the first period with the Jets on the power play after Sean Couturier was called for high-sticking Bryan Little at 18:56.
"I don't think he knows how to panic," Flyers captain Claude Giroux said. "That's a good thing. When you're 20 years old and you have that composure and confidence, it's impressive."
Varone, who gave the Flyers a 1-0 lead at 9:47 of the first period, started the season with Hart with Lehigh Valley of the American Hockey League. He said the goalie he's seeing now is even better against tougher competition.