ARLINGTON, Texas — The Dallas Cowboys knew for a past few years that they possessed talent, especially on offense. Putting it together was the problem.

So far this season, problem solved.

Quarterback Tony Romo threw three touchdown passes, running back DeMarco Murray made history, and the Cowboys won their sixth in a row, beating the New York Giants 31-21 Sunday afternoon at AT&T Stadium.

Dallas (6-1) hasn’t lost since Week 1 and is alone atop the NFC East. The Philadelphia Eagles (5-1) are a half-game back following a bye.

The Giants (3-4) dropped their second straight after a three-game winning streak. New York heads into its bye week looking to regroup.

Romo completed 17 of 23 passes for 279 yards, with two of his three scores going to backup tight end Gavin Escobar. Murray added 128 yards on 28 carries, his seventh consecutive game with triple-digit rushing yardage to open the season, breaking the league record previously held by Hall of Famer Jim Brown.

Giants quarterback Eli Manning threw three touchdown passes, two of them caught by wide receiver Odell Beckham Jr., a rookie first-round pick. Manning’s fourth-down scoring pass to Beckham pulled the Giants within 28-21 with just over five minutes left.

“We just didn’t sustain many drives,” Manning said. “I thought we had a couple of opportunities really in the third quarter where we had some good drives going. Got some first downs and converted some third downs.

“We got to about the 35-yard line and start going backwards. Had penalties, bad plays, losing yardage on runs. Got to give them credit for making some plays.”

Dallas was able to run out the clock before sealing the win on kicker Dan Bailey’s 49-yard field goal with 59 seconds left.

“We’re pretty good in those situations either being able to come back or close out teams,” Romo said.

Dallas receiver Dez Bryant caught nine passes for 151 yards. Escobar, who came into the game with three touchdowns in his career, made three catches passes for 65 yards.

“We really have a bunch of guys who really do things well,” Romo said. “Obviously, DeMarco is at the high level at his position. Dez is at the highest level of his position. … We’re a balanced team that can get the ball to a lot of different people.”

The Giants lost two turnovers, both in the fourth quarter. Another apparent fumble was disallowed after officials ruled forward progress had been stopped.

What the Cowboys said:

“That might have been the best game I’ve ever seen Tony Romo play.” — Owner Jerry Jones

“This is the best we’ve ever been on third down. That’s really changing the game.” — Quarterback Tony Romo

What the Giants said:

“I think the original reaction is to panic. I think this team is sticking together. We have nine games left and nobody wins this division in October.” — Cornerback Prince Amukamara on being 3-4.

What we learned about the Cowboys:

1. Third down is no reason to worry. Dallas came into the game as the NFL leader in third-down efficiency, and converted 9-14 against the Giants.

2. The running game continues to excel. The NFL’s leading rushing team pounded out 156 yards, including 128 from rushing leader DeMarco Murray. Dallas able to control the clock once again, holding the ball for nearly 34 minutes.

–RB DeMarco Murray set the NFL record for consecutive 100-yard rushing games to open a season with seven. He had 128 yards against the Giants on 28 carries. Murray held the previous record of six games with Hall-of-Fame legend Jim Brown.

–TE Gavin Escobar caught a career-best two touchdown passes against the Giants. The second-year backup came into game with only three scores in his previous 22 games.

–QB Tony Romo has thrown a touchdown pass in 35 consecutive games. He finished with three scores.

What we learned about the Giants:

1. Turnovers stymied New York with the game on the line in the fourth quarter. Tight end Larry Donnell fumbled the ball away twice after making catches over the middle. The first miscue helped Dallas take a 14-point lead.

2. After averaging 35 points during their three-game winning streak, the struggles are back. The loss of wide receiver Victor Cruz is a major reason. The Giants were only 5-13 on third down.

–DT Cullen Jenkins suffered a calf strain in the first quarter and was out for the remainder of the game. “You hope it’s not that long,” he said when asked if the injury could be long term. “Obviously, we have a bye week coming up.”

–CB Prince Amukamara had a 38-yard interception return that set up New York’s go-ahead score in the second quarter. “Interceptions are always the spark,” he said. “When the offense scored right after that, the defense just needs to help them more.”

–LB Jon Beason left the game in the first half after aggravating the toe injury he suffered in the spring. He had a full week of practices, but the latest setback is a concern even with the bye week coming up.