Williams attended and played college football at the University of Nebraska. After sitting out during his freshman season, he helped the Cornhuskers go undefeated in 1994 and win their first national championship. The Cornhuskers went undefeated again in 1995 and won another championship. ESPN named the 1995 Nebraska Cornhuskers one of the greatest teams of all time. They scored 638 points (53.2 per game) while only allowing 164 (14.5 per game) on their way to their second consecutive national championship by defeating favored Florida Gators, 62-24. The 1994 and 1995 Nebraska teams, which went a combined 25–0, remain the only undefeated and untied - as well as the only consensus - back-to-back national champions since the University of Oklahoma in 1955 and 1956.