Washington was drafted fourth overall in the first round of the 1976 NFL Draft by the San Diego Chargers. A knee injury forced him to miss the entire 1976 season for the Chargers. In 1977 he played sparingly, appearing in 13 games while rushing for 217 yards and having 244 yards receiving. A month prior to the start of the 1978 season, he was traded to the Baltimore Colts for 3 time Pro Bowl running back Lydell Mitchell.
Baltimore Colts
In 1978, his first year with the Colts, he had 958 yards rushing, which was a career high. In 1979 he led the NFL with 82 receptions. He also had 750 yards receiving and 884 yards rushing along with seven touchdowns. This led Washington to being voted to the 1979 Pro Bowl. His most memorable performance was on September 18, 1978 in Baltimore's 34–27 victory over the New England Patriots on Monday Night Football, when he had a hand in three of the four touchdowns scored by the Colts in a fourth quarter in which both teams combined for 41 points. He helped lead off the scoring by throwing a 54-yard option pass to Roger Carr. Washington followed that up with a 23-yard touchdown catch from Bill Troup. Washington broke a 27–27 deadlock by scoring the game-winner on a 90-yard kickoff return in a driving rainstorm. It was scored in the final seconds of the game after the Patriots came back from 27–13. He remains the only NFL player to ever throw a touchdown, catch a touchdown and return a kickoff for a touchdown in a single game.
Washington Redskins
On April 28, 1981, the Washington Redskins obtained Washington by trading a second-round pick in the 1981 NFL Draft to the Baltimore Colts. During his first year with the Redskins in 1981, Washington combined with future Hall of FamerJohn Riggins to give the Redskins a formidable running game. Washington led the team in rushing with 916 yards and receptions with 70 to go along with 558 yards receiving. The strike shortened 1982 season was mostly a disappointing season for Washington as he only recorded 190 yards rushing during the 9 game regular season and only touched the ball seven times during the Redskins run through the playoffs where they defeated the Miami Dolphins in Super Bowl XVII. Washington returned to his normal dual threat capabilities in 1983 as he recorded 772 yards rushing and 454 yards receiving as the Redskins returned to the Super Bowl only to lose Super Bowl XVIII to the Los Angeles Raiders. During the 1984 season, Washington only played in 7 games for the Redskins and recorded 192 yards rushing.
Atlanta Falcons
He was traded to the Atlanta Falcons during the 1985 NFL Draft and finished his career with one season in Atlanta. During the 1985 season with the Falcons, Washington appeared in all 16 games while recording 210 yards rushing and 37 receptions for 328 yards. Washington retired with 4,839 rushing yards and 3,413 receiving yards and 30 touchdowns in his career.
Post-football career
He had worked as a financial adviser for Wells Fargo. With former basketball player Julius Erving, Washington fielded a NASCAR Busch Series team from 1998–2000. In May 2007, Washington returned to the University of Oklahoma, to serve as the special assistant to the director of athletics/executive director of the Varsity O Association.
