Glass made his stage debut at the Guthrie Theater in Minneapolis before moving to Hollywood. His earliest TV appearances include episodes of Sanford and Son in 1972, an episode of All in the Family in 1973, an episode of The Bob Newhart Show, and episodes of Good Times in 1974. In 1975, he landed the role of Det. Ron Harris in Barney Miller which ran until 1982. The following season, Glass also co-starred with Demond Wilson on television in the short-lived remake of The Odd Couple, called The New Odd Couple. In 1992, he co-starred in the short-lived sitcom Rhythm and Blues, a kind of “black WKRP“, playing “the fifth Top” opposite Roger Kabler. In 1996, Glass was cast as uptight history teacher Roland Felcher in the NBC sitcom Mr. Rhodes opposite comedian Tom Rhodes. In 1999, he appeared in an episode of the NBC sitcom Friends as Ross Geller’s divorce lawyer, Russell.
Since then, Glass has appeared in dozens of television series, including sitcoms such as Family Matters and the series Teen Angel where he played God’s cousin Rod. He was in Star Trek: Voyager (in the episode “Nightingale“) and the science fiction series Firefly (2002), in which he played Derrial Book, a Christian Preacher, or Shepherd, with a mysterious past. Glass himself is a Buddhist. Glass reprised his role from Firefly in the film Serenity (2005). Glass also provides the voice of Randy Carmichael for the Nickelodeon series All Grown Up! and Rugrats and the character Garth in the video game Fable II. In 2008 he appeared in the film Lakeview Terrace alongside Samuel L. Jackson, and starred in the 2010 version of Death at a Funeral as Duncan.