Michael Amadio extended his goal streak to three games, and Linus Ullmark made 20 saves for the Senators (7-5-3), who are 5-1-3 in their past nine.
"That was a tight checking game," Ottawa coach Travis Green said. "Both teams defended hard. I really liked the start of our game; I thought we came out fast. And I thought they pushed back, like a good team will do in their own building. And we found a way to get two points."
Matvei Michkov and Jamie Drysdale scored for the Flyers (8-5-2), who won their previous two games. Christian Dvorak had two assists, and Samuel Ersson made 10 saves.
"This is two games now that the other team comes out stronger than us and out-battles us and makes it hard on us to come back," Philadelphia captain Sean Couturier said. "But as much as it could've been a frustrating day, we didn't give them a whole lot after the first. It was still a big point."
Stutzle gave Ottawa a 1-0 lead at 5:14 of the first when he one-timed a pass from David Perron over Ersson's right shoulder from just below the right face-off dot.
"I've got to do a better job of getting the team ready," Flyers coach Rick Tocchet said, "because we're chasing after that. Like, we obviously didn't like our first, and then after that, I mean, it's a good hockey team, what was it, three shots [against] in the last two periods? I mean, that's hard to do against anybody, and Ottawa's a good team."
Amadio made it 2-0 at 6:19. He took a centering pass from Claude Giroux, skated in from the slot and beat Ersson glove side with a backhand shot.
"I'm fortunate enough to play with two good players right there," Amadio said of his linemates, Giroux and Shane Pinto. "We're just clicking, and we seem to be getting some bounces going our way. It's been a lot of fun."
Michkov cut it to 2-1 at 11:23 of the second period. He shook off a check from Jake Sanderson, drove to the slot and beat Ullmark over the glove with a snap shot.
"What 'Mich' did is something that we're preaching all the time," Tocchet said. "That was textbook. And then what it does, we want to attack the interior, not just defer to the point all the time. … That strong side winger, he goes, 'What do I do?' He was worried about the point shot and then Mich takes the middle and shoots from the interior. That's a perfect example. That'll be in the video room tomorrow on how you want to do it."