Jamie Langenbrunner scored twice and Scott Gomez and Mike Rupp once for New Jersey, which rallied from a 4-1 second-period deficit to force the shootout. Brodeur finished with 26 saves and got the benefit of two goalposts for the Devils (3-3).
Peter Forsberg had three assists and Simon Gagne scored twice for the Flyers. Geoff Sanderson and Mike Knuble also scored.
Robert Esche made 26 saves for Philadelphia (1-5), which lost its fourth straight game.
Brodeur stopped Sanderson with his blocker on the first shootout attempt. Jeff Carter missed the net on the second and Forsberg got off a weak shot on the third.
Brylin scored on the Devils' second shot, beating Esche with a backhander. Esche had stopped Gomez on the first attempt.
Down 4-1 late in the second period, Langenbrunner started the Devils' comeback by taking a pass from Travis Zajac and beating Esche.
Gomez narrowed the gap to a goal with a power-play tally 40 seconds into the third period and Rupp tied the game at 4-all, putting in his own rebound with 9:50 to go in regulation.
Forsberg had set up three straight goals after Langenbrunner tied the game at 1-all early in the second period.
With the Flyers enjoying a two-man advantage, Forsberg found Knuble between the circles for a 2-1 lead at 6:25.
Gagne got the other two goals in a 2:37 span. Using Forsberg as a decoy, he beat Brodeur from above the right circle for a 3-1 edge. He then scored from between the circles for his fourth goal of the pre-season.