Gushchi reached the peak of his career in 1968, beginning with a national shot put title outdoors with a put of 19.60 m. This brought him selection for the event at the 1968 Summer Olympics in Mexico City. At the competition he broke the Soviet record with his first throw in the final, recording 20.09 m to become the first Soviet man to clear the twenty metre mark. This feat brought him the Olympic bronze medal behind Americans Matson and George Woods. He could not repeat this performance later, managing only sixth place at the 1969 European Athletics Championships. He took a second Soviet shot put national title in 1970.