Elliott finished with 97 yards in the Cowboys' 27-17 win, giving him 1,102 this season.
Tony Dorsett had previously owned the record with 1,007 yards in 1977 to help lead the Cowboys to a 12-2 record and a win in Super Bowl XII. Dorsett finished the season with 208 carries and had 12 rushing touchdowns to go along with 29 catches for 273 yards and one receiving touchdown.
Dorsett was on hand to congratulate Elliott on the record:
The No. 4 pick in this year's draft, Elliott entered Sunday leading the NFL with 1,005 yards on 198 carries to go along with nine rushing touchdowns in nine games. He also has 18 catches for 250 yards and one receiving touchdown.
"It feels great," Elliott said after the game. "It means a lot. We've got a great front. They go out there and pave the way and run their tails off. They make it easy for me in certain ways.
"It means a lot with the pedigree of this position playing for the Dallas Cowboys. It means a lot to me to go out there and break a record. It's one step more to where we want to be. One step more to greatness."
Only DeMarco Murray, currently with the Titans, needed fewer games to reach 1,000 yards in a season in team history. Murray reached 1,000 yards in eight games two years ago. Hall of Famer Emmitt Smith, the NFL's all-time leading rusher, needed nine games to reach 1,000 yards in 1995.
Elliott is just the third rookie in NFL history to reach 1,000 yards in nine games, joining Eric Dickerson (1,096 in 1983) and Adrian Peterson (1,081 yards in 2007). Elliott set an NFL rookie record with four straight games of at least 130 yards rushing earlier this season.
Elliott entered Sunday's game just off the pace of Dickerson's rookie record of 1,808 yards for the season.
Elliott breaks Dorsett's Cowboys rookie rushing record
Ezekiel Elliott secured his place in Dallas Cowboys history after an early 2-yard carry allowed the RB to surpass Tony Dorsett's team rookie rushing record of 1,007 yards in 1977.