The Predators had won five games in a row, a streak that has pushed them into contention for the best record in the Western Conference.
Philadelphia had a 2-0 lead heading into the third period thanks to goals by Simmonds in the first and Matt Read in the second. Ryan Suter broke through for Nashville 8:37 into the final period, but Simmonds restored the two-goal lead with 4:41 to play and Claude Giroux scored into an empty net with 1:05 remaining.
The goal for Giroux was his 19th of the season, but his first since Jan. 2.
Bryzgalov finished with 26 saves. Anders Lindback allowed three goals on 27 shots.
Notable deaths of 2014 [PHOTOS]