Jamie Benn scored twice for Dallas, which lost its fourth straight. The Stars began the day two points behind Phoenix for the final wild-card spot in the Western Conference.
Simmonds scored his second of the game with 7:39 left to put Philadelphia ahead 3-1. Just 30 seconds later, Benn scored his second of the contest.
Raffl provided some insurance for Philadelphia by beating Thomas with a backhander on a breakaway with 3:12 to play.