ST. LOUIS — For the Dallas Cowboys, it was a comeback of historical proportions.

For the St. Louis Rams, it was one that got away.

Overcoming a 21-0 second-quarter deficit Sunday, Dallas took the lead for good with two touchdowns in a 15-second span of the fourth quarter and scored a 34-31 win at the Edward Jones Dome.

“We put ourselves in position to win,” St. Louis left guard Rodger Saffold said, “and then we shot ourselves in the foot with mistakes and questionable calls.”

The Cowboys (2-1) tied their largest comeback in franchise history. They were down 21 before beating New Orleans in overtime in 1984, then erased a 21-point margin in 1991 against Washington.

Dallas coach Jason Garrett credited offensive coordinator Scott Linehan for not abandoning the game plan, even after the Rams (1-2) stuffed running back DeMarco Murray for one yard on his first six attempts.

“We kept trying to establish the line of scrimmage, even though they were devoting a lot of defenders to take away the run,” Garrett said.

Murray, who rolled up 428 yards in his first two games against St. Louis, got the run going with 14- and 20-yard bursts late in the second quarter, setting up his 1-yard plunge with 2:07 left in the first half that got the Cowboys on the board.

After pulling within 21-10 at halftime, Dallas started the third quarter with a 68-yard touchdown pass from quarterback Tony Romo to wide receiver Dez Bryant. Because of play action and what appeared to be a defensive breakdown, Bryant was at least 10 yards behind any defender when he caught the ball.

“It was my move that got me that open,” Bryant said. “It was my focus and listening to the coaches. I learned that move from (wide receivers) coach (Derek) Dooley.”

The teams traded field goals — the Cowboys’ Dan Bailey nailed a 40-yarder and the Rams’ Greg Zuerlein connected from 28 — to make it 24-20 St. Louis with 13:28 remaining. Romo then led an 84-yard drive that melted 7:15 off the clock, converting a third-and-13 with a 16-yard scramble, then a third-and-14 with a 20-yard pass to wide receiver Terrance Williams.

Three plays after Bryant drew a 33-yard pass interference foul from cornerback Janoris Jenkins, Romo and Williams teamed up for a 12-yard score with 6:13 left, giving Dallas its first lead of the day.

Romo finished 18 of 23 for 217 yards and two scores, amassing a passer rating of 116.8.

“I thought Tony was more spontaneous today,” Garrett said. “By that, I mean he moved around in the pocket, made some throws on the run. He looked more like himself.”

What the Cowboys said:

“The biggest thing we needed to do was to drive the ball down and get points. The best way to do that is to have balance.” — Coach Jason Garrett.

What the Rams said:

“Game like that, we have to finish. Put that on the defense.” – Defensive end Robert Quinn.

What we learned about the Rams:

1. QB Austin Davis followed up his first NFL win with another good outing, although his pick-six to LB Bruce Carter ultimately proved very costly. Davis completed 30 of 42 passes for 327 yards and three TDs, showing the willingness to hang in until the last second and take the punishment in order to make a play. Davis got eight receivers involved and continues to make a case to be the starter even after Shaun Hill (thigh) returns to full strength.

2. Where’s the pass rush? St. Louis notched 105 sacks in the previous two seasons, but has one so far in three games. They got close to Tony Romo a handful of times and appeared to nail him once, but a debatable holding call on Eugene Sims — who had the sack — nullified it. The defensive backfield, which is missing starting cornerback Trumaine Johnson, can’t hold up unless the front seven is sacking the quarterback.

What we learned about the Cowboys:

1. Instead of panicking after falling behind 21-0, Dallas stuck with its game plan and was rewarded with the win. The Cowboys kept running the ball and RB DeMarco Murray delivered, finishing with 100 yards on 24 attempts after gaining only one on his first six carries. That kind of sensible approach hasn’t been seen very often with this franchise in the last two decades, but the willingness to give a plan time to work sure paid off in this one.

2. Dallas also used the aggression of the St. Louis secondary against it. Employing the deep pass frequently during its comeback, it connected on a 68-yard TD pass 2:12 into the third quarter from QB Tony Romo to Dez Bryant, and also drew pass interference fouls of 26 and 33 yards to set up other TDs. The big plays downfield were a product of the Cowboys’ strong running game and an offensive line which largely kept Romo upright.

PLAYER NOTES

RAMS

–WR Tavon Austin (knee) was one of the team’s inactives Sunday. Austin, who was injured in the second quarter of last week’s 19-17 win in Tampa Bay, should have a good chance to play Oct. 5 in Philadelphia. St. Louis has its bye next week.

–QB Shaun Hill (thigh) went through pregame warmups but never played as Austin Davis threw for 327 yards and three TDs in a losing effort. It doesn’t seem so automatic that Hill will regain his starting job Oct. 5 at Philadelphia, not after Davis has given this offense a jolt of electricity.

–TE Jared Cook led the Rams’ receiving corps with seven catches for 75 yards, but dropped a TD pass early in the fourth quarter that would have expanded St. Louis’ lead to 28-20. After the play, he then shoved QB Austin Davis on the sidelines and had to be restrained by DE William Hayes.

COWBOYS

–LB Bruce Carter (head) was sidelined for part of the third quarter while undergoing evaluation for a possible concussion. He was allowed to return for the fourth quarter and made a huge play, picking off an Austin Davis pass and going 25 yards for what turned out to be the winning TD.

–QB Tony Romo shrugged off an early pick-six to St. Louis’ Janoris Jenkins and made winning plays in the fourth quarter. He extended the go-ahead drive with two third-and-long conversions, eventually throwing a 12-yard TD pass to WR Terrance Williams with 6:13 left. Romo was 18 of 23 for 217 yards, rolling up a 116.8 QB rating.

–TE Jason Witten was a bit more involved in the passing game than he had been the first two weeks, making four catches for 49 yards. Witten has served primarily as a blocker with the team committing to more of a power running game with RB DeMarco Murray.