Washington excelled at Boys and Girls High School in Brooklyn and he was the nation's most sought-after recruit in 1983. When Washington, a point guard, committed to Syracuse, coach Jim Boeheim said the program was changed forever.
Washington's most memorable moment at Syracuse came on Jan. 21, 1984. With a home crowd of 30,293 watching, Washington made a running 45-foot shot at the buzzer to give the Orange a 75- 73 win over Boston College. Washington, who finished with team-high 20 points and seven assists, held both his arms high in triumph as he sprinted off the court and straight into the tunnel leading to the locker room. With the win, Syracuse remained the only undefeated team in the Big East.
"We never had a shot like that for or against us in my 15 years at Syracuse," Boeheim told The New York Times on Jan. 23, 1984. "When I got home, I couldn't go to sleep, so I watched the replay of the Virginia-Clemson game and then watched Washington's shot five or six times. The more I watched, the more I thought it was a miracle. But Dwayne makes miracles happen. He thinks he can make every shot he takes. He hasn't been playing like a freshman but like a veteran who has played the game all his life."
Washington earned All-America recognition at Syracuse from 1984 through 1986. He was named first-team All-Big East three times, and he was the conference tournament's most valuable player in 1986. He led the Orange in assists and steals during each of his three seasons with the school. Syracuse was 71-24 when Washington was with the team.
In 1986, Washington was the No. 13 overall pick by the New Jersey Nets in the NBA draft. Washington played two seasons with New Jersey, averaging 8.6 points and 4.2 assists per game in 1986-87 and 9.3 points and 3.0 assists per game in 1987-88. He played his final NBA season with the Miami Heat in 1988-89, after the Heat selected him with the 17th pick in the 1988 expansion draft. Washington averaged 7.6 points and 4.2 assists per game that season. For his career, Washington had 256 steals and 733 assists in 194 games.