Džajić was just 18 when he was first named to the Yugoslav national team. He made his debut on 17 June 1964 in a 2–1 defeat against Romania at the JNA Stadium in Belgrade. Džajić would go on to earn 85 caps (the most in the history of the Yugoslav national team) and score 23 goals. He became renowned for his passing, dribbling and goal-scoring. His most famous international match was likely the 1968 European Championship semifinal against England, in which his 87th-minute lob over the goalkeeper Gordon Banks gave Yugoslavia a 1–0 victory against the defending world champions. The British press dubbed him "the magic Dragan." He went on to score in the final against Italy but he could not prevent Yugoslavia losing 2–0 after a replay.