Haydn Fleury scored the lone goal for the Jets (35-32-12), who had won three straight.
Connor Hellebuyck allowed five goals on 20 shots before he was replaced by Eric Comrie to begin the third period. Comrie made one save in relief.
Winnipeg is five points behind the Los Angeles Kings, who shut out the Edmonton Oilers 1-0 on Saturday, for the the second wild into the Stanley Cup Playoffs from the Western Conference.
“It is tough because we know how tight it is and the situation we are in where we need points desperately,” Jets defenseman Josh Morrissey said. “At the end of the day, regardless of the score today, we move on and continue to try and control our fate. We have three games left and we have a road trip here and all we can do is try and control what we can control and that is being ready to go against Vegas. There are six possible points left.
"The message is, I think, no one wants to lose like that. It was embarrassing in our own arena. But at the same time, what are we going to do, sit around and cry about it? We have three games left and a huge back-to-back, a tough road trip. Turn the page, fly there tomorrow and get yourself ready to go and let's bring it to the next game. The score hurts right now, embarrassing right now as we drive home, we have to turn the page and keep pushing like we have been.”
Porter Martone gave the Flyers a 1-0 lead at 1:17 of the first period after stealing the puck from Winnipeg forward Adam Lowry inside the defensive zone. Konecny spun around in the high slot on the ensuing rush and passed to Martone, who scored with a sweeping one-timer at the left side of the crease.
“I actually, I almost turned it over,” Konecny said. “And then I knew he was somewhere over there, and it just happened to be probably a lucky play that it went right on his tape, to be honest with you.”