Dryden Hunt made it 2-0 at 9:32, scoring off the rush after getting the puck from Panarin, whose cross-ice pass went through the middle of the zone untouched. Hunt scored after making an inside move on Flyers defenseman Ivan Provorov in the right face-off circle.
Kreider extended the lead to 3-0 at 34 seconds of the second period with a shot from between the hash marks while falling down.
Scott Laughton's turnover in the defensive zone led to a quick passing sequence from Trouba to Zibanejad to Kakko to Kreider.
"It happened fast," Kakko said. "I just saw him and he gave me one right before, but I didn't score. I gave it back to him."
Hunt was assessed a five-minute major for charging Philadelphia defenseman Justin Braun and a game misconduct at 1:56.
Philadelphia had the puck in the offensive zone for almost the entire power play, but New York killed the penalty with Shesterkin making seven saves, leading to a loud "Igor, Igor, Igor" chant from the crowd.
"It's honestly hard to describe," Shesterkin said. "It adds a lot of emotion, a lot of strength. It motivates me. The most important thing is to try to not cry right then and there."
The Flyers have scored 12 goals in the past seven games, with one goal on 19 power plays.
"We need to find a way to finish and we didn't do that," Vigneault said. "Just like we need to find a way to win a game and we didn't do that. The power play had opportunities, could have made a big difference in helping us come back. We're just not making the plays we need to make."
The Flyers cut it to 3-1 at 9:37 when Frost poked a loose puck under Shesterkin for his first goal of the season. But the Rangers limited them to seven shots on goal in the third period after giving up 16 in the second.
Panarin scored into an empty net with 44 seconds left for the 4-1 final.
NOTES: Flyers forward Joel Farabee left the game during the stoppage after Hunt's goal with an upper-body injury, the result of crashing hard into the boards and having Rangers defenseman K'Andre Miller inadvertently slide into him. Vigneault said Farabee will be re-evaluated Thursday. … Philadelphia forward Kevin Hayes had two shots and was minus-2 in 19:49 in his return from missing six games because of an abdominal injury. … Zibanejad's assist on Kreider's goal was his 300th point (140 goals, 160 assists) for the Rangers in his 343rd game with them.