Romo went 28-of-47 through the air for 317 yards, two interceptions and a touchdown pass to Terrance Williams, giving him 20 consecutive games with a scoring strike.
Philadelphia signal-caller Nick Foles, filling in for Michael Vick (hamstring), was also dealt an injury after completing just 11-of-29 passing for 80 yards.
Foles lasted three quarters before exiting with a possible concussion.
Barkley then took over behind center, making good on 11-of-20 passes for 129 yards as the Eagles (3-4) dropped a club-record ninth straight home game.
Celebrity Families of 2014 [PHOTOS]