He was awarded a full scholarship to attend the University of Southern California (USC) in the US, by Head Coach George Toley, who quickly identified Osuna as a major talent.

Described as an "agile and cerebral player"[4] who "moves on the tennis court with the grace of a panther" (Tony Mottram), his subsequent achievements include: Osuna was known for his footspeed, touch, and tactical awareness.

Commentator Bud Collins dubs him "Mexico's greatest player...Ubiquitous on court, confusing to foes, ever seeking the net".

[7] His U.S. Open victory came against big server Frank Froehling, a dangerous unseeded opponent who had upset top-seeded Roy Emerson in the semifinals.

In fact, Osuna climbed the wall of the stadium to retrieve smashes and float back perfect lobs, frustrating Froehling with his nimble speed around the court, touch and tactical variations.

[10] Osuna was one of 79 people killed in the crash of Mexicana de Aviación Flight 704 on 4 June 1969 near Monterrey, Nuevo León, "Pico del Fraile", Tres Cerros.