Martínez came to New York City to study at the Juilliard School at the Lincoln Center for Performing Arts. He also studied acting and gained small parts in several films in the late 1940s and early 1950s. In 1954, he made his first television appearance as himself on The Colgate Comedy Hour, again as himself. He again appeared as himself with his band, Tony Martinez and His Mambo, in the 1956 musical picture Rock Around the Clock. For his role on The Real McCoys, Martínez was discovered by the producer-writing team of the brothers Irving Pincus (1914–1984) and Norman Pincus (1906–1978), while Martínez was performing at a club in Hollywood, California. Martínez sang and played five instruments. Kathleen Nolan, as Kate McCoy, one of the last two surviving members of The Real McCoys cast, recalls that Martínez failed to contact the Pincus brothers because he thought that their interest in his talent was merely a joke, but the producers pursued Martinez and signed him to the cast. Nolan, president of the Screen Actors Guild from 1975–1980, called Martínez’s selection “a major breakthrough in terms of minority representation on television. It may not have been the representation that we are seeking now, but it certainly was a breakthrough to have a major character on television that was not white… He was just a natural, and he had this enormous sense of comedy timing.” Nolan noted too that the Pepino character despite the stereotype was “wise” and often used common sense to help the McCoys resolve their family squabbles.

After The Real McCoys folded, Martínez appeared as a guest star in only a few other television programs, such as The Man from U.N.C.L.E., F Troop, My Favorite Martian, and the 1970 series Storefront Lawyers, renamed Men at Law. In the middle 1960s, Martínez began appearing for nearly 40 years and 2,245 performances of the role of Sancho Panza in Man of La Mancha on Broadway, based on Miguel de Cervantes’s novel Don Quixote. He played opposite a dozen men in the role of Don Quixote, including Richard Kiley and Jose Ferrer. Beginning in 1967, Martínez participated in a national tour of the Tony Award-winning musical. In the early 1980s, Martínez was the executive director of the Institute of Motion Pictures, the government film commission of Puerto Rico. In Nevada, where he spent his later years, Martínez used “PEPINO” for his vanity license plates. His last television appearance was at the age of eighty in the spring of 2000 in The Real McCoys Reunion, broadcast by the former The Nashville Network. Martínez died of natural causes at the age of eighty-two in a hospital in Las Vegas. He had five children, David, Renee, Christian, Lisette, and Kimra. At the time of his death, he had been married for twenty-one years to Myra Martinez of Las Vegas. In addition to Kathleen Nolan, Lydia Reed, who played Tallahassee “Hassie” McCoy, is the other surviving cast member of The Real McCoys. The series featured Walter Brennan in the starring role of Grandpa Amos McCoy, Richard Crenna as Luke McCoy, and Michael Winkelman as Little Luke, the younger brother of Luke McCoy. Andy Clyde and Madge Blake played a popular brother-sister team, George and Flora MacMichael.