|Date of birth||26 August 1958|
|Place of birth||Sarajevo, SFR Yugoslavia|
|Height||1.79 m (5 ft 10 in)|
|2008–2009||Hajduk Split (assistant)|
|2011||Hajduk Split (assistant)|
|2016||Hajduk Split (assistant)|
|* Senior club appearances and goals counted for the domestic league only|
Born in Sarajevo, Socialist Republic of Bosnia and Herzegovina, Socialist Federal Republic of Yugoslavia, Vujović started his professional career with HNK Hajduk Split, making his first division debuts at just 18 and going on to score more than 100 goals in the league (172 overall in 420 matches), while often partnering his brother Zoran. He helped his first club win one league in 1979 and one cup five years later, also being named Yugoslav Footballer of the Year in 1981 by the Večernji list daily.
In 1986, both siblings moved to compete in France, first with FC Girondins de Bordeaux: in their first season both were undisputed starters in an eventual double, as Zlatko also scored in the 2–0 cup win against Olympique de Marseille.
Vujović continued to net with at excellent rate until he retired in 1993, playing in both the first and second levels, with AS Cannes, Paris Saint-Germain FC, FC Sochaux-Montbéliard and OGC Nice. He earned 70 caps and scored 25 goals for the Yugoslavia national team, making his debut on 1 April 1979 in a 3–0 win against Cyprus for the UEFA Euro 1980 qualifiers, and was included in the squads for the 1982 and 1990 FIFA World Cups while also playing Olympic football in 1980.
In 2008, Vujović (as had his brother the previous year) began a coaching career, starting as assistant manager at his first club, Hajduk. He began his third stint in July 2016, when he joined Marijan Pušnik's staff but he left the club in December 2016 after Pušnik was sacked.