"We never blinked, I can honestly say that," Bryant said.
Romo has 21 comeback victories in the fourth quarter or overtime, a franchise best.
"Tony went out there and did what Tony do," Bryant said. "He was poised and he knew what he wanted to do."
Dallas also rallied from a 21-point deficit in 1984 against New Orleans and 1999 against Washington, although both of those wins came in overtime.
It tied the second-largest lead blown by the Rams (1-2), who slowed Murray but got burned everywhere else. Among other breakdowns was a flubbed snap by center Scott Wells, who didn't realize Austin Davis was in the shotgun, resulting in a lost fumble, and a dropped touchdown pass by Jared Cook that could have put the Rams up 28-21. They settled for a field goal.
"I feel like I let this game slip through my hands and it's my fault," Cook said.
St. Louis is 0-2 at home and was whipped 34-6 by Minnesota in the opener. Fisher said Davis played well, but that Shaun Hill would be the starter after the upcoming bye week.
"So, we've got some work to do and some time to look at what we're doing," Fisher said. "They played very, very hard. But they didn't play very smart."
Murray had 100 yards on 24 carries and lost a fumble for the fourth straight game dating to last season, even after switching from carrying the ball on his left side to the right. Three of his 10 career 100-yard games are against the Rams and all leading to victories, with a franchise-record 253 yards in 2011 and 175 yards last season.
Romo was 4 for 5 for 40 yards and scrambled 16 yards on third-and-13 on the go-ahead drive. His second-half play overshadowed a third costly INT of the year.
"We were able to execute under pressure or whatever you want to say, blah, blah, blah," Romo said. "We got it done."
NOTES: The Cowboys are 2-1 for the fourth straight season and have won 12 in a row in Week 3. ... Former Rams great Isaiah Robertson was introduced on the sideline in the first quarter. ... Murray is among four Cowboys to begin a season with a rushing TD in the first four games. Emmit Smith did it four times, Marion Barber three times and Calvin Hill once.
Copyright 2014 by The Associated Press