Mason turned back Craig Smith in the first round of the tiebreaker and made a sprawling leg save on Matt Hendricks in the second.
In between, Vincent Lecavalier beat Marek Mazanec with a forehand shot as the Flyers recorded their first win at Nashville since March 21, 2000 -- a span of five games.
Sean Couturier and Claude Giroux each scored in regulation for Philadelphia, which began a six-game road trip with the victory.
Mazanec finished with 22 stops.
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