Baeza began his racing career in 1955 in Panama at Hipodromo Juan Franco, and in March 1960, was invited to Miami, Florida to ride under contract for Owner/Trainer, Fred Hooper.
[3] Two years later, he rode to his first Kentucky Derby victory on Chateaugay, as well as for his second Belmont Stakes win.
[4] In 1969, he won the Belmont for the third time, denying Majestic Prince the Triple Crown, on board Paul Mellon's future Hall of Famer, Arts and Letters.
In 1972, Baeza travelled to York Racecourse in England, where he rode John Galbraith's Roberto to victory over the previously unbeaten Brigadier Gerard in the inaugural Benson & Hedges Gold Cup.
That same year, he went to Woodbine Racetrack in Toronto, Ontario, Canada, where he won the prestigious Canadian International Stakes on Droll Role for Trainer T. J.Kelly.