Couturier scored 43 seconds into the first period to make it 1-0 on a tic-tac-toe play with Claude Giroux and Travis Konecny.
Hintz tied the game 1-1 at 7:00 of the first. He took a pass from Benn, skated around defenseman Matt Niskanen, and beat Hart.
Esa Lindell tipped a pass from Denis Gurianov for a power-play goal to give Dallas a 2-1 lead at 13:48 of the first.
The Stars were 1-for-25 on the power play before the goal.
"That was a tough game in a tough building against a good team," Benn said. "... We got it done, Bishop played great. Two points is all we really wanted, we don't really care how we did it. We got these two points, and we're going to move on here."
The Flyers outshot the Stars 39-16 and out-attempted them 64-39.
"You look at the scoring chances and the shots, obviously we had quite a bit more than they did, and there's some things to like about that," said Philadelphia forward James van Riemsdyk, who had nine shots on goal. "... We're going to have to find a way to generate more goals because obviously, again, when you score one goal, you're not going to win too many games."
Perry scored with a backhand at 1:24 of the third period to make it 3-1.
"He was unreal," Stars coach Jim Montgomery said. "Three games in four nights, his first three games of the year. Very impressive by him. Skilled, poised. Adds character, a little snot to us, and obviously skill. … Flyers were sitting here waiting for us at home. ... Those guys dug in, give them credit."
Miro Heiskanen scored into an empty net with 1:55 remaining for the 4-1 final.
