The Maksimir club played its first match in UEFA competitions on that day, September 10, 1958. At that time, there were two continental competitions: the European Cup under UEFA's authority and the Inter-Cities Fairs Cup under FIFA's umbrella. Both competitions were established in 1955, with the European Cup evolving into the Champions League, while the Inter-Cities Fairs Cup transferred from FIFA to UEFA in 1971, changed its name to the UEFA Cup, and later became the Europa League. The third major continental club competition was the Cup Winners' Cup, which ran from 1960 to 1999.

Dinamo thus recorded its first official appearance in one of these three pan-European competitions in the summer of 1958. This, of course, does not count earlier participations in the Central European Mitropa Cup.

The Blues were champions of Yugoslavia in the 1957/58 season and as such entered the first round of the European Cup where they faced Dukla Prague. The first leg was played on September 10 in Zagreb, with the return leg on October 1 in Prague.

Dukla was, naturally, the champion of then-Czechoslovakia and also the backbone of the national team. As many as seven of their players had participated in the World Cup in Sweden, which had ended just a month and a half earlier. Dinamo had five of their own 'recruits' among the 22 players in the Yugoslav national team at the same World Cup: Gordan Irvović, Tomislav Crnković, Ivan Šantek, Luka Lipošinović, and Dražan Jerković.

In the match played in rainy weather, Dukla led 2-0, but the Blues eventually managed to secure a draw.

The visitors took the lead in the 30th minute when goalkeeper Gordan Irvović rushed out, and Jaroslav Borovička somehow managed to push the ball past the post and into the goal. In the 52nd minute, Jan Brumovsky pounced on a ball that rebounded off the post and hammered it into the net from the edge of the penalty area.

The Blues came back with two goals in the space of three minutes, from the 70th to the 73rd. Luka Lipošinović was the scorer on both occasions. First, Vladimir Čonč sent the ball forward, Lipošinović received it, ran in front of the goalkeeper, skillfully rounded him, and pushed the ball into the net. Shortly after, Dražan Jerković played a short pass to Lipošinović in the penalty area, who fired into the net from a run for the equalizer.

In the return leg in Prague, the home team won 2-1 and progressed. The Blues were led from the bench by former popular half-back Gustav Lechner.

Interestingly, the delegate for this match was Gusztav Sebes, the former celebrated coach of the Hungarian national team, the famous 'Magical Magyars', during their greatest glory days.