Radek Faksa and Brett Ritchie scored, and Kari Lehtonen made 31 saves for the Stars. Lehtonen is 2-11-3 against Philadelphia in his NHL career.
"I think it gives us confidence," Lehtonen said. "It's our job to go out there and play our hearts out, and we need to just keep doing that."
Mrazek made 20 saves. He is 5-5-3 since joining the Flyers at the trade deadline, and 13-12-6 this season.
"We had lots of chances, lots of opportunities," Mrazek said. "I think this time of the year we have to get those bounces on our side."
Faksa gave Dallas a 1-0 lead at 10:50 of the first period with his 15th goal of the season. He took a rebound off the end boards behind the net and backhanded the puck off the left skate of Mrazak, who was skating across toward the near post.
Konecny tied it 1-1 at 16:51 with his 23rd goal of the season. He carried the puck from the left point to the right circle and sent a wrist shot to the glove side of Lehtonen.
Philadelphia took a 2-1 lead at 2:03 of the second period on Ivan Provorov's shot on the rush from the slot that went over Lehtonen's blocker for his 14th goal of the season.
Ritchie's power-play goal tied it 2-2 at 10:11. A shot from the right circle by Radulov grazed the blocker of Mrazek and was redirected by Ritchie at the crease.