The matchup of MVP candidate quarterbacks seemed headed for overtime, but Mark Andrews bobbled away a conversion pass that would have tied the game.
Barkley broke free for two long touchdown runs and Philly held off a late Rams rally to advance to a matchup with Washington for the conference title.
Hurts has a week to recover and get ready for next Sunday's NFC championship game against the Commanders.
Patrick Mahomes drew a couple of controversial calls against Houston.