The win, and a break in the schedule, could propel the Cowboys back in the thick of the division race. They will play five of their next six games at home, starting Sunday against Cleveland.
"Don't use words like desperate," Romo said. "The importance was at its highest level. I don't know if we are thinking anything more than we need another win."
The latest game between these fierce rivals was more about salvaging a season than playing with something big on the line.
The loss could speed up the countdown clock on Vick's and Reid's time in Philadelphia.
Foles hit the field in the second quarter and was greeted by a loud ovation from a crowd that had become fed up with Vick's erratic play.
Vick did not talk to reporters but appeared groggy in the locker room.
Reid said he'd determine the starter for Sunday's game at Washington based on Vick's health.
"I was hoping he'd make it through without having a concussion, but that's where we sit right now with him," Reid said.
Foles was rolling, the Eagles were scoring, and the good times were back at Lincoln Financial Field.
Romo, who finished 19 of 26 for 209 yards, tied it with that TD pass to Bryant.
Owner Jerry Jones refused to call the win a season saver.
"I don't want to do that," he said. "You can, but I don't want to do it. I know how important the game is to us."
Early in the final quarter, Foles had an interception return for a touchdown wiped out on a holding penalty. No worries, Dallas. Harris returned a punt 78 yards for a 24-17 lead that silenced the crowd.
On the next drive, Foles had an interception returned for a score that counted, by Carr, returned 47 yards for a 31-17 lead.
That was it for the fans in green, who fled for the exits. Stanley Havili had a 1-yard TD run with 1:55 left, but Henery missed the extra point.
"Critical win for us," Garrett said. "I thought the effort was there. I thought we were focused the whole game. When you have success, you have to play through it, you have adversity, you have to play through it, and today was a good example of that."
In the final minutes, fans behind Dallas' bench unrolled a banner that read, "Andy, Quit, Your Team Has!"
Foles was 22 of 32 for 209 yards and one touchdown.
"Not good enough to win," Foles said. "I made some mistakes and I can't turn the ball over. That's the most important thing to win games."
Vick, the four-time Pro Bowl quarterback, has struggled this season and entered with 10 touchdowns and nine interceptions.
NOTES: Foles was the first Eagles rookie QB to throw a TD pass since AJ Feely in 2001. Brian Westbrook, a running back, threw one in 2002. ... The Eagles had won six straight division games, including a sweep of the Cowboys. ... Eagles WR Jason Avant left with a hamstring injury. ... Sims started 15 games for the Eagles in 2010 and had two sacks.