He won the US Open men's singles title in 1975, beating the defending champion Jimmy Connors in the final.

On 7 September 1975 Orantes defeated top-seeded Jimmy Connors in the final of the US Open at Forest Hills, New York to win his only Grand Slam title.

Overall, he won 36 singles titles, including Rome (1972), Hamburg (1972 & 1975), Canada (1975), Monte Carlo (1975), the U.S. Claycourt Championships (1973, 1975 & 1977), the U.S.

He also reached 35 finals, including the French Open (1974), Cincinnati (1973), Monte Carlo (1970), Canada (1973 & 1974), Rome (1973 & 1975), and Hamburg (1976 & 1977).

He reached 20 doubles finals, including the French Open in 1978, Canada in 1976, and Hamburg in 1973.