Sloane made his Broadway debut in 1935, playing Rosetti the agent in George Abbott's hit comedy, Boy Meets Girl. Everett eventually joined Orson Welles' Mercury Theatre, and acted in Welles' films in roles such as Bernstein in Citizen Kane in 1941 and Arthur Bannister in The Lady from Shanghai in 1947. He played an assassin in Renaissance-era Italy opposite Welles' Cesare Borgia in Prince of Foxes (1949).
Sloane also worked extensively in television; in November 1955 he starred in the Alfred Hitchcock Presents episode "Our Cook's a Treasure"; he appeared on the NBC anthology series The Joseph Cotten Show, also known as On Trial, in the 1956 episode "Law Is for the Lovers", with co-star Inger Stevens.
In 1961, Sloane appeared in an episode of The Asphalt Jungle. In the early 1960s, he voiced the title character of The Dick Tracy Show in 130 cartoons. Beginning in 1964, he provided character voices for the animated TV series Johnny Quest. He also starred in the ABC sci-fi television series Voyage to the Bottom of the Sea, in the episode "Hot Line". He wrote the unused lyrics to "The Fishin' Hole", the theme song for The Andy Griffith Show. Sloane guest starred on the show in 1962, playing Jubal Foster in the episode "The Keeper of the Flame". He starred in both the film and television versions of Rod Serling's Patterns, and in the first season of The Twilight Zone in the episode "The Fever".