With the Flyers deprived of leading scorer Claude Giroux due to a one-game suspension, the Devils simply smothered the life out of Philadelphia's offense to seal the series 4-1.
Brodeur, who made 27 saves, guided New Jersey to their last Stanley Cup triumph in 2003 and the Devils are once again playing like Cup contenders.
The Flyers were held to just 11 goals over the five games.
"(Brodeur) played great again tonight," New Jersey's Zach Parise said. "When we have a breakdown he's there to bail us out. We have to give a lot of credit to our defenseman too."
Philadelphia opened the scoring in the first period through Maxime Talbot but Bryce Salvador and David Clarkson responded to give New Jersey a 2-1 lead midway through the period.
It marked the fourth straight game in the series that the Flyers grabbed the early lead only to lose it.
Ilya Kovalchuk added a third-period goal from a slap shot to cap the scoring and set up an Eastern Conference showdown against either the New York Rangers or Washington Capitals.
"I just appreciate all the work of the doctors and trainers," said Kovalchuk, who was forced to sit out of Game Two of the series with a lower-body injury.
"We'll see who is going to win (the Capitals-Rangers series) and I can't wait for the Conference Finals."
Under first-year coach Peter DeBoer, who was fired from Florida in 2011, the Devils have played with a renewed toughness this season and it showed in their handling of physical Philadelphia.
The Flyers signed goaltender Ilya Bryzgalov in the off-season in an attempt to cure their recent playoff shortcomings. Bryzgalov finished with 27 saves in the season finale but in the end Philadelphia did not produce enough offense to prevail.