Brozović began his career with local sides JŠK and HŠK Zrinjski Mostar before moving to Građanski Zagreb in 1935. With Građanski he won the Yugoslav championship in 1937 and 1940. He debuted for the Kingdom of Yugoslavia's national team in 1940. However, with the establishment of the Independent State of Croatia in 1941 he began playing for the Croatian national team. He suited up for Croatia 17 times during the war before communist Yugoslavia came into existence after the war. The Communist authorities disbanded Građanski Zagreb, forcing Brozović to move to the newly formed army club, FK Partizan, with which he won the Yugoslavian championship and the Yugoslavian cup in 1947.