Norris is tied for fifth in the NHL with 12 power-play goals and has seven goals in his past eight games.
Tim Stützle scored, Connor Brown had two assists, and Anton Forsberg made 28 saves for the Senators (22-34-5), who ended a three-game losing streak.
Cam Atkinson scored, and Martin Jones made 33 saves for the Flyers (19-31-11), who have lost 12 straight road games (0-10-2).
"He played great for us," Atkinson said of Jones. "Their first couple goals were absolute snipes. He kept us in the game all night and [gave] us a chance to win. That's what you need out of our goalies, and they've certainly been doing that for us as of late."
Flyers captain Claude Giroux was a healthy scratch amid multiple reports he could be traded before the 2022 NHL Trade Deadline on Monday at 3 p.m. ET.
Philadelphia coach Mike Yeo said he noticed Giroux's absence on the power play and during 4-on-4 situations.
"And now some other people get some opportunities," Yeo said. "I'm not going to blame [the loss] on that by any means. It's something that people are going to have to figure out. They're going to have to embrace it. The bottom line is, if you're a gamer, you want those situations, you want those minutes, you want those opportunities."
Ottawa forward Nicholas Paul, who has also been the subject of trade rumors, was a late scratch.
"Real hard," Smith said of telling Paul he wasn't in the lineup. "Nick's obviously a guy that everyone loves and who is a huge part of the group in there. It's part of the business and it's an unfortunate one. It happens all around the league."
Stutzle gave the Senators a 1-0 lead at 10:45 of the first period when he picked the top left corner with a wrist shot from the left face-off dot. The forward has scored nine points (two goals, seven assists) in his past eight games.
"He was flying" Smith said. "He was dangerous, he checked, he worked away from the puck. I mean, that line was dangerous all night, and led by him. He had all kinds of chances. I always wish he'd shoot more because I don't think he believes how good he can shoot it."