As a graduate student at the Kiev Institute of Physical Culture, Borzov studied films of great sprinters to determine optimal sprinting techniques such as the best push-off angle and the most effective body incline at the breakaway. He won the European 100-metre sprint championship in 1969, 1971, and 1974; the 200-metre European championship in 1971; and seven European indoor titles. At the 1972 Olympic Games in Munich, after his two chief American challengers missed their qualifying races, Borzov won a gold medal in the 100-metre dash in 10.14 seconds. In the 200-metre he won a second gold medal in 20.0 seconds. He also anchored the Soviet team that won a silver medal in the 4 × 100-metre relay.

At the 1976 Olympics in Montreal, Borzov again ran the 100-metre sprint in 10.14, but this time won only a bronze medal; he also ran in the 4 × 100-metre relay, in which the Soviet team won a bronze medal. Ankle injuries prevented him from participating in the 1980 Olympics in Moscow. He married the great Soviet gymnast Lyudmila Ivanovna Turishcheva (Turishcheva, Lyudmila Ivanovna).