[2] In 1964, Baylon and her teammate Helga Schultze reached the final of the doubles event at the 1964 French Championships, losing in straight sets to Margaret Smith and Lesley Turner.

At the 1964 Wimbledon Championships, she reached her first quarterfinals after defeating seventh-seeded Jan Lehane in the third round, but she retired against first-seeded Margaret Smith.

Later that year at the U.S. National Championships, Baylon was seeded eighth, and she was defeated in the quarterfinals by third-seeded Nancy Richey.

At the 1966 U.S. National Championships, Baylon was seeded sixth and again reached the quarterfinals in which she won just a single game against second-seeded and eventual champion Maria Bueno.

[4] From 1964 to 1966, she played in four ties for the Argentine Fed Cup team, winning three matches and losing four.