Morin put the Flyers ahead 2-1 with 4:27 remaining in the third period. The Rangers turned over the puck in their end and Flyers forward Nicolas Aube-Kubel passed the puck back to Morin, whose shot from the point got past Shesterkin.
Selected by Philadelphia with the No. 11 pick of the 2013 NHL Draft, Morin was playing his 15th NHL game and second since being moved back to defenseman. The Flyers shifted the 25-year-old to left wing during training camp and he played four games there earlier this season.
Morin was limited to 28 games between the NHL and the American Hockey League in 2017-18 and 2019-20 because of a core muscle injury and twice tearing the ACL in his right knee.
"It's been a hard couple of years for me," Morin said. "I was just trying to take it day by day. ... I got a lot of support here with the Flyers, good teammates, good family. Worked hard, and now I'm there and I'm trying to stay in the lineup."
Elliott said, "It's pretty special. This guy's been through a lot within the organization, a lot of injuries and surgeries, and he's always come back with a smile on his face every day, ready to work, can't wait to get back on the ice with the guys. I think that's why everyone was so happy. When you work so hard and guys can see it and he brings energy every day no matter if he's in the lineup or not in the lineup, it's something special. It rubs off on the guys and we're just so happy for him."
Zibanejad scored on the power play to put the Rangers ahead 1-0 at 10:54 of the first period. It was his seventh goal in the past three games against the Flyers. He scored six points (three goals, three assists) in each of the previous two games against Philadelphia, including an 8-3 win by New York on Thursday.
The Flyers trailed 6-0 in the second period Thursday but kept the Rangers from building their lead Saturday.
"They were on us, on the [defensemen], pretty hard, taking away the walls," New York defenseman Jacob Trouba said. "Tough to really get a handle on the puck and make a good, quality breakout. So a lot of grinding breakouts and not a lot of tape-to-tape breakouts, which obviously we prefer to do."
Patrick redirected a shot by Shayne Gostisbehere on the power play to tie it 1-1 at 12:52 of the second period. It was his second goal in his past 26 games.