Zybina's mother and brother perished from starvation and exposure during World War II, a fate she witnessed and to which she almost succumbed. By 1950, however, she was a major force in track-and-field throwing events, holding Soviet records in the javelin, sport grenade, and shot put. Between 1952 and 1956 she set 14 Soviet shot put records.

Zybina won a gold in the shot put at the 1952 Olympics in Helsinki, Finland, with a put of 15.28 metres (50 feet 1.75 inches). She competed in the shot put at the next three Olympics, winning a silver at the 1956 Games in Melbourne, Australia, and a bronze at the 1964 Games in Tokyo.