Artemi Panarin had a goal and an assist, Jacob Trouba and Dryden Hunt also scored and Kaapo Kakko added two assists as the Rangers won for the eighth time in nine games. New York has won six in a row at home.
"The first 10 games (of the season) I'd say we weren't playing well but we found a way to get points," Rangers coach Gerard Gallant said. "The last 10 games I got no issue with the way we played. Tonight was a tougher one. ... We had four days off between games and it just didn't feel right."
Shesterkin made 11 saves in the first period, 15 in the second and seven in the third to improve to 12-3-2 with a 2.15 goals-against average this season. He was serenaded with chants of "I-gor! I-gor! I-gor!" throughout the game, especially in the second period when he made seven saves during the Flyers' five-minute power play.
"It's honestly hard to describe. It adds a lot of emotion, a lot of strength," Shesterkin said through a translator. "It motivates me, definitely. The most important thing is to try to not cry right then and there."
Morgan Frost scored and Carter Hart had 24 saves for Philadelphia, which lost its seventh straight (0-5-2). The Flyers went 0 for 3 on the power play and have just two goals in their last 37 chances.
"We're just not making the plays we need to make," coach Alain Vigneault said. "I'm not satisfied about anything. We have to find a way to win games here. This is serious. We're not scoring right now, we're not finishing. We're going to have to find a way to win games 1-0 or 2-1 until we get some of that finish that I know some of these players have. Right now we're not seeing it, we're not executing it."
Trailing by two, the Flyers pulled Hart with about 2 1/2 minutes remaining and Panarin scored an empty-netter with 44 seconds left for the final margin.
Kreider made it 3-0 just 34 seconds into the second period, getting a centering pass from Kakko at the right doorstep and firing it past Hart while falling down for his team-leading 16th goal of the season. No other Rangers player has more than five. Mika Zibanejad also had an assist on the play for his 300th point with the Rangers.
The Flyers went on the power play less than 90 seconds later as Hunt was whistled for a charging major. After a review, he also received a game misconduct that carries an automatic ejection. Shesterkin denied Scott Laughton's tip try, and slap shots by Cam Atkinson, Keith Yandle and Claude Giroux.
"I thought (that) power play gave us some momentum," said Vigneault, who coached the Rangers from 2013-18 and took them to a Stanley Cup final. "We had some real good looks. At the end of the day you need to find a way to finish and we didn't do that. Just like we need to find a way to win a game, and we didn't do that tonight also."
Frost finally got the Flyers on the scoreboard at 9:37 of the middle period as he knocked in a loose puck after Giroux's shot bounced around in front off several players. It came on Philadelphia's 21st shot of the game.
The Flyers had a short-handed breakaway early in the game but Shesterkin made a glove save on Joel Farabee's slap shot from the left circle at 2:39.
Just more than a minute later, Trouba scored on a give-and-go with Kakko as he fired a one-timer from the point off the return pass for his fourth at 3:41.
The Rangers made it 2-0 at 9:32 as Hunt got a pass from Panarin along the right side, cut toward the net, moved the puck from his backhand to forehand while being defended by Ivan Provorov, and fired it past Hart for his third goal. Adam Fox got his 18th assist - most among NHL defensemen.
Former Rangers C Kevin Hayes returned to the Flyers' lineup after missing six games with an abdominal injury. Derick Brassard, another former Rangers player, remained out of the lineup with a hip injury.
Farabee left in the first period after falling awkwardly into the boards and didn't return.
Barclay Goodrow left about seven minutes into the third period after the puck deflected up into his face. He was down on the ice briefly before skating off and heading to the locker room, putting the Rangers down two forwards.
Each team was playing after having the previous game at home postponed due to the New York Islanders' COVID-19 outbreak, the Rangers on Sunday night and the Flyers on Tuesday. The Rangers were coming off a 5-2 win at Boston last Friday, and Philadelphia lost 5-2 at New Jersey on Sunday.
Flyers: Host Tampa Bay on Sunday.
Rangers: Host San Jose on Friday night.
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Kreider scores Rangers' third goal while falling to the ice
Chris Kreider lights the lamp 34 seconds into the second period to increase the Rangers' lead.