Washington attended Chicago's John Marshall Harlan Career Academy, before receiving a football scholarship to play for Morgan State University. He was coached by Earl Banks, who at the time sent many of his players to professional football. He became a four year starter at cornerback and was part of a team that had 31 straight wins. As a senior, he was named co-captain, posted 6 interceptions and received All-CIAA honors. He finished his career with 15 interceptions. In 1993, he was inducted into the Morgan State University Athletic Hall of Fame.
Washington was selected by the Dallas Cowboys in the 13th round of the 1970 NFL Draft. Even as a rookie, he was one of the best athletes on the team and showed his big play potential with a 100-yard kickoff return for a touchdown against the Washington Redskins. He also blocked an extra point in Super Bowl V. His 48.4 yards per kick return that season remains a franchise record. Coming into his second year, he injured his knee while returning a kickoff in preseason and was waived injured on August 25, 1971. He would eventually rejoin the team and play in two games. When Herb Adderley retired in 1973, he had a chance to earn the left cornerback starting job, but he was passed over by Charlie Waters. After Waters struggled, he replaced him the next year and started 6 games. In 1974, he was named the starting left cornerback at mid-season and held the job until being slowed down by an ankle injury in the last 2 games. In 1975, he was the starter at left cornerback for the full season, registered 4 interceptions and helped the Cowboys reach Super Bowl X. But he is mostly remembered for his play against Lynn Swann, who finished the game with four receptions for a then Super Bowl record 161 yards, one touchdown and became the first wide receiver to earn Super Bowl MVP honors. Washington had excellent coverage on Swann on all 4 receptions, but Swann was able to make plays each time. The next year, he was replaced with Benny Barnes, but got a chance to start 5 games at right cornerback after Mel Renfro was injured, posting 4 interceptions. In 1977, he started 4 games at mid-season after Aaron Kyle suffered a fractured left wrist. He also filled in at left corner in Super Bowl XII when Barnes exited with a foot injury early in the game. In 1978, he started 3 games at left cornerback in place of Barnes who had foot problems, but was later sidelined himself by a right knee injury. He was waived on August 21, 1979.
