Vargo officiated in the World Series in 1965, 1971, 1978 and 1983, serving as crew chief in 1978. He worked the NLCS in 1969 (the first NLCS), 1973, 1976 and 1980, and the All-Star Game in 1961 (first game), 1966, 1974 and 1981. He was the home plate umpire for Game 4 of the 1971 World Series, the Fall Classic's first night game.