Born in Ivanjica, Kovačević moved to Belgrade in 1955 and joined the youth system of Partizan. He was promoted to the first team in 1958, making his official debut in a 2–1 home league win over Rijeka. During the next eight seasons, Kovačević helped Partizan win the Yugoslav First League on four occasions (1960–61, 1961–62, 1962–63, and 1964–65). He was also a member of the team that lost the 1966 European Cup Final to Real Madrid. Two years earlier, Kovačević was the competition's joint top scorer with seven goals, along with Sandro Mazzola and Ferenc Puskás.