Nelson was selected by the Minnesota Vikings in the 1st round (7th overall) in 1982 NFL Draft after graduating from Stanford University. He spent eight 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.
Nelson was actually traded from the Vikings to the Cowboys as part of the infamous Herschel Walker Trade in 1989. However, after refusing to report to Dallas, he was subsequently traded to the San Diego Chargers for a fifth round draft choice.
As a running back, Nelson was a threat as both a runner and as receiver out of the backfield, though he is perhaps best known for dropping the game-tying touchdown on 4th down in the closing moments of the 1987 NFC Championship Game. 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. Nelson worked as a Senior Associate Athletic Director - External Relations/Development for his alma mater, Stanford University. He now works in a similar capacity at UC Irvine. He attended Pius X High School, Downey, California. Nelson was elected to the College Football Hall of Fame in 2014. Nelson was the first running back in college football history to rush for 1,000 yards and catch 50 passes in the same season; he accomplished this feat three times in his college career.