Before appearing on television, Washington trained and performed at the New Federal Theater in New York, a theater founded to provide opportunities to minorities and women. Early in his acting career, Blacque began making guest appearances in sitcoms such as What's Happening!!, Sanford and Son, The Bob Newhart Show, The Tony Randall Show, Good Times, and Taxi, and auditioned for permanent roles on others, including Venus Flytrap on WKRP in Cincinnati, eventually played by Tim Reid.
In 1981 he joined the cast of the fledgling police drama Hill Street Blues, staying with the show throughout its run, which ended in 1987. While appearing on that show, he was nominated in 1982 for the Emmy for Outstanding Supporting Actor in a Drama Series, but lost to fellow HSB actor Michael Conrad, in the only year in which all the nominees in a category came from the same series. His theatrical career continued during his run on the show, winning him an NAACP Image Award of Best Actor (Local) in 1985 for his role in Amen Corner; in 1986, his stage roles included the male lead in the musical Don't Get God Started during its initial six-week summer run in Beverly Hills.
After Hill Street ended, Blacque moved to Atlanta, Georgia, to provide a better home for his children; in his new home, he has focused on theatrical work while making occasional guest appearances on television. Notable stage performances include Stepping Into Tomorrow with Yolanda King in 1987 and a 1988 revival of Ceremonies in Dark Old Men. Television work included a pilot, Off-Duty, for CBS, in which Blacque once again played a police officer; the show was not picked up by the network. Blacque also had a small role in Disney's animated film Oliver & Company.
Blacque initially was asked to serve as spokesperson for the County of Los Angeles Adoption Services office though he had no adoptive children at the time. Upon looking into adoption, he was told that as a single black male, he was not eligible to adopt; however, he pressed on, eventually adopting ten children in addition to the two sons he already had. The adopted children included twin boys and a group of five children whose mother could not keep them due to her drug addiction. In 1989 he was asked by President George H. W. Bush to serve as a national spokesperson for adoption.
