Horvath was the youngest player to win the National American Junior Tennis Championships (age group 16 years and younger). In addition, she is the only player to win the youth championships on clay, the US Girls Clay Courts , in all four age groups in a row. In 1980 she also won the junior women competition at the French Open .
Horvath played on the WTA Tour from 1981 to 1989 . During this time she won five singles and three doubles titles and in 1984 moved up to 10th place in the world rankings . She achieved her greatest successes in Grand Slam tournaments in 1983 and 1984 at the French Open, when she reached the quarter-finals there. In 1983 she was the only player who could beat Martina Navrátilová (6: 4, 0: 6, 6: 3 in the round of 16 of the French Open).