Johnston gave Dallas a 1-0 lead at 4:02 of the first period when he stole the puck off the stick of Scott Laughton in neutral ice and shot it past Ersson from the top of the left circle.
Tyler Seguin extended it to 2-0 at 7:52 after a point shot from Stars defenseman Ryan Suter landed at his feet and he shot it five-hole from the top of the crease.
Joel Farabee cut it to 2-1 at 10:12, deflecting a rebound on the back doorstep of the crease past a scrambling Wedgewood.
“The bench was good all night,” Flyers coach John Tortorella said. “We’d been coming back all night long, never really had the lead. They just kept on playing. It’s one of the things we talked about before the game is, especially in this building, they can get it revved up pretty good here.
“You’ve just got to handle some of the momentum swings and just keep playing. I really liked how our team handled itself as far as just staying with themselves and finding a way to crawl back in.”
Konecny tied it 2-2 at 16:36 on a short-handed breakaway that began after Cates broke up a Stars offensive zone entry at the blue line.
“I think the stats had the turnovers 13-1, I think that’s being generous for us,” Dallas coach Pete DeBoer said. “I think our puck management was horrendous. That’s the great equalizer. You can do everything else right, but if you’re going to mismanage the puck, your [defense] can’t keep gaps because they don’t trust the forwards are going to get it in.
“That’s what it looks like. We’ve got to figure that out. We’re a smarter team than that. We’re lucky we didn’t get burnt; [Wedgewood] gave us a game. I guess the silver lining is we’ve got this overtime thing figured out.”