Moses was born in New York City, the brother of actor and singer Burke Moses. As a character actor with appearances on projects ranging as diverse as Big Momma's House 2 (2006), Platoon (1986) and Star Trek: Voyager (1999), Moses was always reliably employed, but never became a household name in America. This changed in 2004, when Moses was cast in the role of Paul Young on the hit ABC dramedy Desperate Housewives (2004-07). As the disturbed husband of the deceased (suicide victim) Mary Alice Young, Moses plays one of the pivotal figures in the show's main mystery.

On May 23, 2006, preview performances began for an Off-Broadway play (co-starring Wendie Malick, Ashley Williams and James Badge Dale) called Burleigh Grimes (which has nothing to do with the baseball player of the same name). He played the title character, "a Wall Street creep" (as per the May 19, 2006 New York Daily News). According to the paper, he and Malick "got deep into character ... when they rang the NYSE opening bell." The play ended on Sunday, July 16, 2006