Bernier gave the Devils a two-goal lead when he scored 67 seconds later. Bernier was open long enough to tap his stick and ask Andrei Loktionov for a pass.
Mason made the initial save, but Bernier shovelled the rebound behind him.
The third goal came with 5:56 left in the second period when Zubrus tipped in a wrist shot from defenceman Adam Larsson.
Cory Schneider stopped all nine Flyers shots he faced through two periods. He wasn't even supposed to play. Martin Brodeur was scheduled to get the start, but flew to Montreal where his father, Denis Brodeur, Sr., died at age 82.
Ryder added an empty-net goal with 1:27 remaining.
Kinkaid finished with three saves on four shots. Mason made 21 saves on 24 shots.