In 1976, Kline left The Acting Company and settled in New York City, doing a brief appearance as the character "Woody Reed" in the now-defunct soap opera Search for Tomorrow. He followed this with a return to the stage in 1977 to play Clym Yeobright opposite Donna Theodore as Eustacia Vye in The Hudson Guild Theater production of Dance on a Country Grave, Kelly Hamilton's musical version of Thomas Hardy's The Return of the Native. In 1978, he played the role of Bruce Granit, a matinée idol caricature, in Harold Prince's On the Twentieth Century, for which he won his first Tony Award. In 1981, Kline appeared with rock diva Linda Ronstadt and singer Rex Smith in the New York Shakespeare Festival's Central Park production of The Pirates of Penzance, winning another Tony Award for Best Leading Actor in a Musical, for his comically dashing portrayal of the Pirate King. In 1983, he played the role in a film version of the musical, also with Ronstadt, Smith and Angela Lansbury, which had a limited theatrical release.