"Hurricane Helen", as the Canadian press dubbed her for her fiery demeanour, achieved a career high WTA ranking of World No. 13 (November 1989), and was a regular fixture in the top-25 between 1986 and 1991. She won singles titles in two tour events, the 1986 Japan Open and the 1988 Citta de Taranto, and was a singles French Open quarter-finalist in 1988 (lost to Gabriela Sabatini) and 1989 (lost to Mary-Joe Fernandez). During her time on the WTA Tour, Kelesi recorded wins over Arantxa Sanchez-Vicario, Conchita Martinez, Jana Novotna, Manuela Maleeva-Fragniere, Helena Sukova and Pam Shriver, and pushed Chris Evert and Monica Seles hard in high-profile matches. She also held a set-point in a 4th Round match at the French Open against Steffi Graf in 1987.
Kelesi's game was characterized by aggressive baseline play, with a powerful top-spin forehand and two-handed backhand. She also retrieved well and could play defensively when needed. These skills meant that Kelesi was particularly good on clay and hard-court surfaces. Her volley and forecourt play was not so instinctive, however, and a missed volley at a crucial stage in a match against Monica Seles illustrated this (Seles won 4–6 6–4 6–4 in a second round match at the 1990 French Open).
Kelesi was a Canadian Federation Cup team member from 1986 to 1993. She was Tennis Canada singles player of the year four times (1986, 1987, 1989, and 1990).
Kelesi's professional career came to an end in 1995 when a brain tumour the size of a tennis ball was discovered following months of headaches, dizziness and vision problems. Numerous operations followed over the years, Kelesi successfully recovered and began coaching young children in Canada in the late 1990s. She also became a part-time tennis journalist and commentator.