Newhouse's son, Rodd Newhouse, says his father died Tuesday at Mayo Clinic in Rochester, Minn., after a battle with heart disease.
Newhouse had suffered a stroke in 2010.
"He had no airs about him at all. Just a genuine, wonderful, really top flight man," said NFL Media's Gil Brandt.
The burly running back was drafted by the Cowboys in 1972 out of the University of Houston, where he ran for 1,757 yards as a senior, a school record that still stands.
In the 1977 Super Bowl victory against Denver, Newhouse threw a 29-yard touchdown pass to Golden Richards on a halfback option to help seal the win.
Newhouse was born in Longview and went to Galilee High School in Hallsville before enrolling at Houston. All three Cougars teams he played on finished the season ranked in The Associated Press Top 20.
Newhouse is survived by his wife, Nancy, daughters, Dawnyel and Shawntel, and sons Rodd and Reggie, who played for the Arizona Cardinals in 2004-05.
The Associated Press contributed to this report.