The game swung in the Devils' favor midway through the second period when Brodeur beat Briere.
With the score tied at 1, Briere broke into the Devils' zone and was hooked by Vitaly Vishnevski. Briere was awarded a penalty shot at 9:32 but Brodeur won the duel with a stick stop, energizing New Jersey.
Only 40 seconds later, Madden got his second of the game, completing a 2-on-1 short-handed rush with Jamie Langenbrunner and the Devils never relinquished the lead.
"That was the turning point in the hockey game," Devils coach Brent Sutter said. "They get the penalty shot and Marty makes a great save. It was massive."
Unlike a shootout, Brodeur had little time to prepare.
"It happens pretty quick," Brodeur said. "It's not like a shootout where they take their time. Right away, the heat goes on and he tries for a shot."
Moments before the penalty shot, Briere tried to beat Brodeur with a rising shot.
"I had a feeling that wasn't the place he wanted to shoot because he had just missed," Brodeur said. "I knew he wasn't going to go high on me."
Briere mistakenly figured he had the element of surprise with a low shot.
"Just before, I tried to beat him high glove and he took it away," Briere said. "I thought he would try for the same thing. When you have a goalie like him, you try to do the unexpected. Very rarely do I go five-hole. I tried to surprise him."
After Madden got the short-handed tally, Arron Asham followed with a shot from the slot at 13:57 as the Devils took a 3-1 lead and control of the game.
"We had three or four good chances to score before they get the short handed goal," Briere said. "Brodeur made the key saves and they had the momentum on their side.
Langenbrunner sealed the win for the Devils, who have won 10 straight from the Flyers in New Jersey, with an empty-netter. Philadelphia last won in New Jersey on March 9, 2004.
Mike Richards and Briere scored for the Flyers, who have lost three straight for the first time this season.
The teams exchanged power-play goals earlier in the second. Richards gave the Flyers the lead 40 seconds in before Madden countered at 2:49.
In the third, Briere put the Flyers back in the game with a power-play goal at 6:44 that cut the Devils' lead to 3-2. That time, Briere beat Brodeur with a high shot.
It wasn't enough to offset the opportunity that slipped away on the penalty shot.
The Devils outshot the Flyers 14-8 in the scoreless first period. Philadelphia had one of the best chances in the closing seconds when Briere's power-play slapper from the blueline almost trickled past Brodeur.
- D Paul Martin returned for the Devils after sitting out Saturday's 4-1 home loss to Phoenix. With Martin back, New Jersey dressed six defensemen after using seven against the Coyotes.
- The Devils head to western Canada for a three game road trip with stops in Vancouver, Edmonton and Calgary.
- Riley Cote and the Devils' Mike Rupp fought 2:03 into the game with Cote getting a quick decision by landing a left hand to Rupp's jaw. In the third, Flyers defenseman Jason Smith and David Clarkson battled to a draw at 2:04.
- Briere and Madden led their teams with 6 shots each.