It's Philadelphia's longest streak since winning nine straight in April 1995.
Schenn had three power-play goals in a 4-2 win over Dallas on Saturday, then scored 2:44 into OT against Detroit for his eighth goal of the season.
Schenn cut in off the left wing, skated across the top of the crease, faked a backhand shot and slid in the winner.
The 22-year-old Stolarz is the youngest Flyers goalie to post a shutout since Dominic Roussell on Feb. 27, 1992. He made 28 saves, helping Philadelphia outlast Jimmy Howard and the Red Wings. Howard made 34 saves in his first start since Nov. 23.
"It's exciting, that's for sure. I couldn't have drawn it up any better and when you're a kid dreaming of playing at Joe Louis Arena," Stolarz said. "It's something you can't even put into words. I'm excited, but I'm more excited to have the win streak going."
The Red Wings got their first point at home since Dec. 1. They have only 20 goals in their last 12 games at Joe Louis Arena, in which they are 2-7-3.
"I thought we did a lot of good things. The only thing that's missing is goals," Red Wings captain Henrik Zetterberg. "I thought we were playing good structure, forechecking well, playing good in our own end. Howie's (Howard) good again. The only thing we were missing is goals."
Howard dropped his goals-against average to 1.68.
"It's not about being perfect out there. I don't think anyone can be perfect," Howard said. "It's about going out there and making saves and making timely saves. It's unfortunate that they were able to get one past me."
Howard stopped Pierre-Edouard Bellemaire from the bottom inside edge of the right circle 1:53 into overtime.
Detroit defenseman Xavier Ouellet and Philadelphia's Michael Raffl got fighting majors 8:03 into the third period. Ouellet got in more punches and received a 2-minute instigator penalty after Raffl landed a hit on Steve Ott.