Lyudmila Khvedosyuk did not take up canoeing until 1958, when she was 22 years old, but in 1960 she won her first of 19 Soviet titles that she would earn through 1973. She captured her first major international title, in the K-2 500, at the 1961 European Championships, and her first World title two years later in the K-4 500. At that tournament, she also won silver in the K-1 and K-2 500 events. Her next stop was the 1964 Tokyo Olympics, where she took home gold in the K-1 500. She was European champion in the K-1 and K-4 500 competitions in 1965, and World champion in those events in 1966. In 1967, she was a triple European champion in the K-1, K-2, and K-4 500 events.
Now competing as Lyudmila Pinayeva, she returned to the Olympics in 1968 and defended her K-1 500 title, in addition to taking bronze in the K-2 500 with Antonina Seredina. She then won the K-1 500 competitions at the 1970 and 1971 World Championships, while also taking the K-4 500 title at the latter edition. She attended her third Olympics in 1972 and won gold in the K-2 500 with Yekaterina Kuryshko. Her final major international medals came at the 1973 World Championships, with gold in the K-4 500 and silver in the K-2 500. Following her retirement, she worked as a sports administrator.