Starting in 1981, Svetlana (from 1984 playing under her married name Parkhomenko) won the senior Soviet doubles championships eight times (twice in 1987).

In 1983, Cherneva won the European amateur championships in women's and mixed doubles and took bronze in the same disciplines at the 1983 Summer Universiade.

In 1984, she won her first ITF titles in San Antonio and Delray Beach, and at the Wimbledon Championships advanced with Savchenko to the quarterfinals, after defeating third seed Kathy Horvath and Virginia Ruzici, as well as Chris Evert and Catherine Tanvier.

In 1987, they reached semifinals at Wimbledon, after defeating the world's best pair, recent Grand Slam winners Martina Navratilova and Pam Shriver.

In 1993, she played three ties for the Russia Fed Cup team, winning her doubles games against Ukrainians and Lithuanians.