Moore studied drama in his native Indiana before serving in the Marines during WWII, during which he participated in the battle for Iwo Jima. Post-war, he furthered his training at the Pasadena Playhouse. Moore succeeded David Wayne in the role of Ensign Pulver opposite Henry Fonda's "Mister Roberts" on Broadway, and later toured with the play. As if life were following art, he made his screen debut playing the quartermaster in "Okinawa" (1952). For much of the 1950s, he was relegated to small roles in features, like his turns opposite Marilyn Monroe in "Gentlemen Prefer Blondes" (1953) and as Mitzi Gaynor's boyfriend in "There's No Business Like Show Business" (1954). Frustrated by his stalled career, Moore supplemented his income by purchasing an interest in an iron foundry that made tile tabletops and considered abandoning his dream. He had one of his better roles as the wisecracking member of a group out to rob a casino in the crime caper "Five Against the House" (1955), co-starring Brian Keith and Kim Novak. While he appeared in support of stars like Gregory Peck and Lauren Bacall in "Designing Woman" (1957) and Jack Lemmon in "The Wackiest Ship in the Army" (1961), his roles remained decidedly supporting. He remained active in features into the 1980s, generally in small parts such as a gas station mechanic in a sheriff in "Dr. Minx" (1975), and a chili salesman in "The Horror Show" (1989), among others. With L Q Jones, he formed a producing partnership that resulted in the above-average thriller "The Brotherhood of Satan" (1971), about a town overtaken by a coven of witches, and the futuristic black comedy "A Boy and His Dog" (1975), starring Don Johnson. Moore also reprised the voice for Grandpa in "Here Comes the Littles" (1985), a feature based on the 1983 ABC animated series.

Moore found his greatest success on the small screen. In 1955, he was the narrator for the ABC series "Border Collie" and that same year appeared as a reporter in the "What I Want To Be" segments of "The Mickey Mouse Club" (ABC). He amassed numerous guest credits on series, including "My Little Margie", "Pete and Gladys", "The Beverly Hillbillies" and "The Andy Griffith Show". Moore remained active into the 1990s, with guest appearances on "Frasier" (NBC, 1994, as a patient) and "The Pursuit of Happiness" (NBC, 1995, as a wedding guest).

In TV longforms, Moore played a distraught father in "Cotton Candy" (NBC, 1978) and the first mayor in "Little House: The Last Farewell" (NBC, 1989). He also revived the character of Hank Kimball in "Return to Green Acres" (CBS, 1990).