Korać was born in Sombor, in the Kingdom of Yugoslavia. He started playing for OKK Beograd, at the age of 16, and played as a left-handed forward-center. Popularly nicknamed, Žućko ('Ginger'), he became one of the best, if not the best, player of the Yugoslav First Federal League in the 1960s. In 1960, Korać was named The Best Athlete of Yugoslavia, and Yugoslav Sportsman of the Year. He was the best scorer of the Yugoslav First Federal League for seven seasons, which was a record. He scored a total of 5,185 points, in 169 games played in the Yugoslav League, for a career scoring average of 30.7 points per game. In 1962, in a Yugoslav First Federal League game against Mladost Zagreb, Korać scored 74 points.[4]
With OKK Beograd, he won four Yugoslav League titles. Korać also played in multiple FIBA European Champions' Cup (EuroLeague) competitions with OKK Beograd. Korać was named a part of the best European selection, in both 1964 and 1965. In a two-game playoff series against Swedish League champions Alviks, during the 1964–65 season of the FIBA European Champions' Cup (EuroLeague), he scored 170 points. He scored 71 points in the first game of the series, and 99 points in the second game of the series, for a series scoring average of 85 points per game.[5] He averaged 54.8 points per game that season, which is the highest single-season scoring average in the EuroLeague's history, since 1958.
He was the Top Scorer of the 1960 Summer Olympic Games,[6] and he won the silver medal at the 1968 Summer Olympic Games. With Yugoslavia's senior men's national team, he scored 3,153 points in 157 games played, for a scoring average of 20.1 points per game.[7] He was the leading scorer in the 1960 games.[8]
In the 2011 Serbian biopic and semi-documentary film Ginger: More Than a Game, Korać is portrayed by Vladimir Aleksić.[9] The film tells the story of his life.[10]
In the 2015 Serbian sports drama We Will Be the World Champions, Korać is portrayed by Dejan Dedić.[11] Dedić also reprised his role in the 2016 Serbian TV series Prvaci sveta.[12]