Nelson was selected by the Minnesota Vikings in the 1st round (7th overall) in 1982 NFL Draft after graduating from Stanford University. He spent 10 seasons with the Vikings; 1982–1989, before going to the San Diego Chargers. Nelson would spend the final nine games of the 1989 season and the entire 1990 season with the Chargers. Following his year and a half away from the Vikings, Nelson returned to the team in 1991 and stayed there for the final two years of his career, 1991–1992.
As a running back, Nelson was a threat as both a runner and as receiver out of the backfield. For his career, Nelson rushed for 4,442 yards, caught 286 passes for 2,559 yards and scored 23 touchdowns (18 rushing and 5 receiving) in 152 games. He is most remembered for his dropped pass on 4th down in the 1987 NFC Championship Game.
As of 2007, Nelson works with Stanford University as a Senior Associate Athletic Director - External Relations/Development.