Živković spent eight seasons at Partizan, before moving to Benfica in 1986. He also played for Fortuna Düsseldorf and Dijon, before retiring in 1991. Živković made five appearances for the Yugoslavia national team and scored two goals. He was also a member of the team at the 1982 FIFA World Cup. +List of international goals scored by Zvonko Živković No. Date Venue Opponent Score Result Competition 1 15 December 1982 Titograd, Yugoslavia UEFA Euro 1984 qualifying 2 29 January 1985 Kochi, India Friendly
Živković was the head coach of the Serbia and Montenegro national under-19 team from 2004 to 2005. With him, they reached the semifinals of the 2005 UEFA European Under-19 Championship. Živković also led the Serbian national under-19 team to the 2007 UEFA European Under-19 Championship.