Šuker's second and the first official match for Croatia came in a friendly against Mexico in 1992 where he scored a brace in a 3–0 victory. He then led Croatia to their first major international tournament, UEFA Euro 1996, with a then-record 12 goals in 10 matches during the qualifying stages. During the Euro 1996 final stages in England, he scored three goals in four matches, including two in the 3–0 group stage win over defending champions Denmark. It was in this match he set up the final score with an unforgettable looping shot over Danish goalkeeper Peter Schmeichel, still remembered as one of the greatest goals in UEFA European Championship history. Šuker's feats during the tournament saw him named to the Team of the Tournament.