Uzun was born on 6 June 1950 in Kayacık, in the Turhal district of Tokat. He began mat wrestling in 1965 with the Turhal Sugar Factory team under coach Mevlüt Yıldırım, and later continued under Mehmet Gocur and Hasan Sevinç.[3]
In 1969, Uzun won the Balkan junior title. The following year, he won his first Turkish senior championship.[3] In 1971, he won the gold medal in the men's freestyle 74 kg event at the 1971 Mediterranean Games and finished fourth at the 1971 World Wrestling Championships.[2][3]
Uzun finished sixth at the 1972 European Wrestling Championships in the 74 kg division. In 1973, he was sixth at the 1973 European Wrestling Championships and fourth at the 1973 World Wrestling Championships. In 1974, after moving up to 82 kg, he placed sixth at the 1974 European Wrestling Championships and won the silver medal at the 1974 World Wrestling Championships in Istanbul.[2]
In 1975, he finished fourth at the 1975 European Wrestling Championships, won the gold medal in the men's freestyle 82 kg event at the 1975 Mediterranean Games in Algiers, and placed sixth at the 1975 World Wrestling Championships. He then finished sixth at the 1976 European Wrestling Championships.[2]
At the 1976 Summer Olympics in Montreal, Uzun finished fourth in the men's freestyle 82 kg event. He lost his opening bout 9–4 to Poland's Henryk Mazur, then defeated Diop of Senegal, István Kovács of Hungary, and Bulgaria's Ismail Abilov to remain in contention. In his final bout, he lost 13–5 to the United States' John Peterson and placed fourth overall.[4][1]
Uzun remained active internationally after Montreal. He finished fourth at the 1977 European Wrestling Championships and the 1977 World Wrestling Championships, and ninth at the 1978 European Wrestling Championships.[2]
He retired from active competition in 1980. Until 1990, he worked as coach of the Turhal Sugar Factory wrestling team and also served at various levels of the Turkish national team coaching staff. In 1988, he was named the most successful wrestling coach of the year by the Turkish Wrestling Federation. In 2008, he was awarded the title of State Athlete.[3]