Guram Minashvili played most of his career, which lasted from 1953-71, with Dynamo Tbilisi, except for his final years, 1968-71 when he was with Sinatle Tbilisi. With Dynamo, Minashvili won the FIBA European Champions Cup in 1962, a Soviet title in 1953, silvers at the Soviet championships in 1959-62, and a bronze at the 1965 Soviet championships. Minashvili was on the Soviet national team from 1957-64 and with them he won a silver at the 1960 Olympics, a bronze at the 1963 World Championships and European titles in 1957, 1959 and 1963. Minashvili also participated at the 1959 World Championships, where the Soviet Union refused to play against Taiwan (Chinese Taipei) and was disqualified. After finishing his sporting career, Minashvili worked with the physical education department of the Georgian Technical University.