As a junior, Yzaga won the French Open in 1985 and reached the semi-finals of Wimbledon (also in 1985) and of the US Open (1984).
Yzaga played on the professional tour from 1984 to 1996, reaching career-high rankings of World No. 18 in singles and World No. 54 in doubles (both in 1989). He was a quarter-finalist at the Australian Open in 1991, and at the US Open in 1994, reaching the final eight by defeating in back-to-back matches finalists of the previous edition: Cédric Pioline and Pete Sampras in 5 sets. Yzaga came back from a 2-sets-to-0 deficit against Pioline and 2-sets-to-1 against Sampras, in both those matches he won fewer points. He had earlier been the first ever opponent of Sampras in the main draw of a Grand Slam tournament, in the first round of the 1988 US Open, also winning that match in 5 sets.
Since retiring as a player, Yzaga has served as captain of Peru's Davis Cup team.