Ray Emery, who was given a game misconduct after his fight with Capitals goalie Braden Holtby on Friday, earned the shutout but needed to make just 14 saves. It was the team's first shutout of the season.
Named the game's first star, Emery said the key was the giveaway department; the Flyers had none.
"I think that is a testament to how much the guys wanted it and how simple we were willing to play and stick to the things we needed to do and play basically mistake-free hockey," Emery said.
The lone goal came when Schenn tipped in a shot by Andrej Meszaros with 5 minutes, 31 seconds remaining in the first period.
It was Schenn's third goal and only the 21st of the season for the Flyers (4-9-0).
Wayne Simmonds started the play by attempting to shoot on net, but the puck bounced to Meszaros.
"I just stopped in front of the net and was at the right place at the right time and was able to get a stick on the puck," Schenn said.
Berube shook up the defense, using Meszaros and Hal Gill, the 38-year-old veteran who was playing his first game for the Flyers since signing as a free agent on Oct. 1.
The move paid off.
In the second period, with the Devils on the power play, Emery stopped Adam Henrique on two close-in shots. Former Flyer Jaromir Jagr just missed scoring on a close-range backhander in the second period.
In the first 10 minutes of the third period, the Flyers were stopped on tip-in attempts by Scott Hartnell and Jake Voracek, keeping the Devils (3-6-4) in the game.
With fewer than five minutes left, the Devils' Michael Ryder hit the post from the left circle after taking a pass from Jagr.
Simmonds shot wide on a breakaway with nearly three minutes to go, but on this night it didn't hurt the Flyers.
Notes. Flyers general manger Paul Holmgren said that he expects Vinny Lecavalier to miss just one game because of a facial bruise suffered during a fight in Friday's loss.
"It's sore," Holmgren said before Saturday's game. "I expect him to play Tuesday [at Carolina]."
There were some reports that suggested Lecavalier had lost teeth, but Holmgren said that wasn't the case.
Holmgren also said any reports that Steve Downie suffered an orbital fracture were not true. Downie has a concussion, suffered during a fight on Friday.
"Steve is a little better today," said Holmgren, who added that Downie is expected to be released from the hospital Sunday.