Murray broke Brown's 56-year-old mark with his seventh straight 100-yard rushing game to start a season, Romo threw three touchdown passes and the Cowboys beat the New York Giants 31-21 Sunday.
Romo had a fourth scoring pass overturned on replay. Instead, Murray wound up with his seventh rushing touchdown of the season on a 1-yard plunge.
He finished with 128 yards on the ground to pass Brown, who hit the century mark in the first six games of the 1958 season for Cleveland.
The Cowboys (6-1) are off to their best start since winning six of their first seven on the way to a 13-3 finish in 2007, when they were the top seed in the NFC before losing to New York in their first playoff game.
Eli Manning had three touchdown passes for the Giants (3-4), who have lost road games to the NFC East's top two teams in consecutive weeks. New York now has two-game skids on either side of a three-game winning streak.
Bryant had a touchdown taken away when he stretched his left arm over the goal line as he was being tackled by Prince Amukamara. The call was overturned on review, and Murray scored on the next play for a 28-14 fourth-quarter lead.
Murray didn't return in the first half after falling down in the open field on his longest run before halftime, a 21-yard sprint around right end. He spent a few minutes with trainers on the sideline but didn't leave the field.
The fourth-year back from Oklahoma returned in the second half and broke Brown's record on a 1-yard plunge early in the fourth quarter after a 15-yard carry put him on the verge of setting the mark.
After the Giants pulled within seven on Odell Beckham Jr.'s second touchdown catch, Murray had seven carries on a time-killing drive to Dan Bailey's 49-yard field goal for a two-score lead with 1:05 to go.
New York tight end Larry Donnell had team highs of seven catches for 90 yards but fumbled twice. The first one set up a Cowboys touchdown for a 14-point lead in the fourth quarter and the second clinched the Dallas victory in the final minute.
Beckham was starting in Victor Cruz's place in the Giants' first game since their star receiver was taken off the field in tears when he tore the patellar tendon in his right knee in last week's 27-0 loss at Philadelphia.
The first score for Beckham was a 9-yard catch for a 7-all tie in the second quarter. The Giants went ahead less than 4 minutes later on Manning's 27-yard pass to Daniel Fells on the first play after Bryant fell on a deep route, giving Amukamara an easy interception that he returned 38 yards.
Manning was 21 of 33 for 248 yards.