Zlatko was born in Maribor, Slovenia, to Serbian parents. He started his career at the youth team of Kovinar Maribor. In 1989 he was noticed by a well known Yugoslav football player Milko Đurovski (who at that time was doing military service in Maribor). He then played for Partizan Belgrade, (1989–1993), including loan spells at Proleter, Zrenjanin (1990–1991); Vitória Guimarães (1993–1996), FC Porto (1996–1999), Olympiakos (1999–2000), Valencia (2000–2001) and Benfica (from 2001 onwards).
His best performances came during his time at Porto. In 2001 his team Valencia reached the Champions League finals, but lost after a penalty shootout against the German champions Bayern Munich. Zlatko was one of the penalty takers to miss; to be more precise, Oliver Kahn superbly saved his shot.
His first match for the Slovenian national team was on November 7 1992 at a friendly match against Cyprus. The Slovenian national team qualified for the 2000 European Championship in Belgium and the Netherlands, where Zlatko played very well, scoring three of Slovenia's four goals.
Slovenia also managed to qualify for the 2002 World Cup in South Korea and Japan but Zlatko had a very serious argument with the Slovenian national coach Srečko Katanec and he was sent home immediately after the first match against Spain.
Srečko Katanec resigned immediately after the World Cup, so Zlatko returned to the national team. He played what was probably his last national team match on April 28 2004 against Switzerland. Altogether he played 80 matches for the national team and scored 35 goals, thus making him the most successful Slovenian soccer player after Slovenian independence.
Zlatko is infamous for his numerous arguments, the one with Srečko Katanec being just the most famous. Soon after, at Olympiakos, he had an argument with the management and he left the club before the season was over. Such were the bad feelings of the Piraeus fans he disappointed that, when Valencia were scheduled to visit Greece for a Champions' League game, he was issued a death threat and did not make the trip with the Spanish side.
Zahovic also had an argument with Valencia coach Héctor Cúper, believing that he was not being given enough opportunities. Nevertheless, he played for Valencia till the end of the 2001 season when he moved to Benfica, who he left in the middle of the 2004/2005 season.