ARLINGTON, Texas — Dallas quarterback Tony Romo threw three touchdown passes, running back DeMarco Murray made history and the Cowboys won their sixth in a row by 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. Philadelphia (5-1) had a bye week, but joins the Cowboys as one of the NFL’s four remaining one-loss teams.

The Giants (3-4) dropped their second straight after a three-game winning streak.

Romo threw for 279 yards and of his three scores, a pair went to backup tight end Gavin Escobar. Murray added 128 yards on the ground, his seventh consecutive game in triple digits to open the season to set a new league record previously held by Hall of Famer Jim Brown.

Giants quarterback Eli Manning had three touchdowns and two were caught by rookie first-round pick Odell Beckham. His fourth-down scoring pass to Beckham pulled the Giants within 28-21 with just over five minutes left.

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.

Dallas receiver Dez Bryant caught nine passes for 151 yards. Escobar came into the game with only three touchdowns in his career before catching three passes for 65 yards.

The Giants suffered three turnovers, including two in the fourth quarter.

The Cowboys broke a 14-14 tie at the half on Escobar’s second touchdown midway through the third quarter. Escobar stretched out to haul in the 26-yard strike over the middle by his fingertips.

Murray gave Dallas a two-score lead with a 1-yard run in the fourth following a lost fumble by New York. Murray has at least one touchdown in six games this season.

The Cowboys took an early 7-0 lead by converting three third downs on their second drive, including Romo’s 15-yard touchdown pass to Escobar. Dallas came into the game as the league leader in third-down efficiency.

New York went up 14-7 in the second quarter thanks to a long drive and a quick strike following a turnover. Both scores were courtesy of Manning throws.

The Giants tied it after a 71-yard drive that included a fourth-down conversion via pass interference. Manning hit Beckham from nine yards out for the score.

Romo was picked off on the ensuing possession trying to throw deep to Bryant, who had fell on the fly patter that cornerback Prince Amukamara fielded like a punt and returned 38 yards to Dallas’ 27. After a play-action fake, Manning hooked up with tight end Daniel Fells for a go-ahead TD.

Dallas’ 80-yard march in 10 plays to respond culminated in Romo’s scoring toss to receiver Terrance Williams in the back of the end zone. Murray picked up 35 yards on the drive.

NOTES: Dallas RB Joseph Randle, caught recently shoplifting underwear and fined nearly $30,000 by the team, is now a spokesman for an underwear company. In a partnership with MeUndies, Randle is donating underwear and apparel to Dallas-area children in need. … Cowboys starters LB Bruce Carter (quadriceps) and RT Doug Free (foot) were inactive. … Cowboys RB DeMarco Murray briefly left the game in the second quarter with a foot injury but returned after trainers re-taped his ankles. … Giants WR Victor Cruz (patellar tendon) had season-ending surgery last Monday. Newly-signed WR Kevin Ogletree, a former Cowboy, was active. CB Dominique Rodgers-Cromartie was also active after being listed as questionable. … It was Dallas’ first game against an NFC East opponent.