Murray rushed for 434 yards with one touchdown while also catching 20 passes for 156 yards as the Cowboys surged to the top of the NFC East with a 4-0 November.
A third-round pick out of Oklahoma, he made his first start of the season on October 23 and rushed for a franchise-record 253 yards with a touchdown on 25 carries.
For the season, Murray has rookie bests of 834 rushing yards and 1,011 yards from scrimmage. He is the fourth Cowboy to win rookie of the month and first since DeMarcus Ware in October 2005.
Miller captured defensive honors after recording 31 tackles with 4 1/2 sacks to help the Broncos to a 4-0 mark for November. His best game of the month came in a 17-13 win over Jets in Week 11 when he registered 10 tackles, three for loss, and 1 1/2 sacks.
The second overall pick of the 2011 draft out of Texas A&M has 10 1/2 sacks this season, surpassing Mike Croel's team rookie mark of 10 in 1991. He leads the AFC and is tied for third in the NFL in sacks.
Miller is the fourth Bronco to be honored as rookie of the month.
Other offensive nominees included October winner Andy Dalton of Cincinnati, who threw for 1,030 yards with seven touchdowns; Washington running back Roy Helu, who accumulated 400 yards from scrimmage with a touchdown; and September winner Cam Newton, who threw for 700 yards with a touchdown and ran for 145 yards with three scores.
Defensive consideration went to Arizona linebacker Sam Acho, who recorded 15 tackles with three sacks, two forced fumbles and a fumble recovery; September winner Ryan Kerrigan of Washington, who totaled 19 tackles with 4 1/2 sacks and two forced fumbles; and Arizona cornerback Patrick Peterson, who racked up 15 tackles, an interception and a fumble recovery while also excelling on special teams with two punt returns for touchdowns.