Williams began his career as a McDonald's High School All-American while attending Paul Laurence Dunbar High School in Baltimore, where he played with fellow NBA players Muggsy Bogues, Reggie Lewis, and David Wingate. The 1981–82 Dunbar Poets finished the season at 29–0 during Williams's junior season and finished 31–0 during his senior season, and were ranked first in the nation by USA Today. He then attended Georgetown University and enjoyed an outstanding collegiate career. In his four seasons at Georgetown, he was amongst career leaders in scoring, rebounding, assists and steals in school history, finishing no lower than seventh in any category. As a freshman, he scored 19 points and grabbed seven rebounds against the University of Houston in the 1984 national championship game which the Hoyas won 84–75. As a senior during the 1986–87 season, Williams was the leader of a young team which became a contender for a national championship. During that season he led the Big East in scoring, and led the team in rebounding, steals and blocked shots, and was third in assists. Because of Williams's play, it led Georgetown coach Thompson to dub the team “Reggie and the Miracles”. The team won a share of the 1986–87 Big East Championship and the Big East Tournament. In the 1987 NCAA tournament, the Hoyas reached the Southeast Regional Final, but lost to Providence College, 88–73.