He won the Tony Award for Best Supporting Actor as Richard Henry Lee in the original Broadway production of 1776, a role he reprised in 1972 for the film 1776.
Roles like the narcissistic Miles Gloriosus in A Funny Thing Happened on the Way to the Forum (which he originated in the show's Broadway premiere) led to him developing a reputation for what Frank Rich called his portrayal of "vain ladies' men.
As an opera singer, Holgate played leading roles in La Boheme, Don Giovanni, and the world premiere of Philip Marshall, among many others.
He had an active career as a concert singer, which included performances at Carnegie Hall and a Broadway revue with his first wife, Dorothy Collins (1926–1994).
Although he had only one song, "The Lees of Old Virginia", and a scant few lines of additional dialogue, he earned that season's Tony Award as Best Featured Actor in a Musical.