After uncertain ties at the start of the competition, when they got past Spartak Brno only thanks to the luck of the draw, a toss of a coin, the Maksimir players turned their attention to a new, demanding opponent. In that second round of the celebrated season, on the road to the Inter-Cities Fairs Cup trophy, a competition that later grew into the UEFA Cup, today's Europa League, the Blues were awaited by Scotland's Dunfermline, whose attack featured the later celebrated manager Sir Alex Ferguson... In the first leg in Scotland, the hosts won 4-2, even though Dinamo had led 2-1.

In the return leg, Dinamo won 2-0, with Slaven Zambata scoring twice. He secured progression by shaking the net 13 minutes from time, giving Dinamo the two-goal margin they needed.

Coach Branko Zebec had difficulties selecting his line-up, above all at left-back. Mirko Charlie Braun was missing because of the red card he received in the first match in Scotland, and Petar Lončarić did not play because of a death in the family... Zlatko Mesić therefore stepped in at left-back.

Dinamo fully controlled the game and dictated the tempo, but without creating any dangerous chances... After half an hour of play, the Blues moved up a gear and soon scored. In the 32nd minute, Krasnodar Rora broke into the penalty area from the left wing, Josip Gutzmirtl received the ball there and passed it short in front of goal, where Zambata appeared. Despite being pressed by two defenders, the Maksimir striker fired the ball into the net from a deft turn.

Towards the end of the first half, the Blues came close to a second goal. Marijan Novak dribbled through the defence on the right wing and swung the ball in front of goal, and Gutzmirtl, diving, headed it towards goal. Scottish defender Roy Barry got his hand to the ball on its way to the net, changing its direction. Hungarian referee Tibor Votava, however, did not point to the penalty spot.

Gutzmirtl threatened again at the start of the second half, unleashing a fierce shot from the left that flew just over the crossbar. The Blues doubled their lead in the 77th minute and finally got the two-goal margin they had so badly wanted. Rudolf Cvek sent the ball from the right to the opposite side, Gračanin picked it up and delivered it into a crowded box, where Zambata, once again surrounded by two defenders, managed to find a path to goal with a low shot for 2-0. The visitors believed Dinamo's striker had been offside, but this time the referee did not side with them. Dinamo could even have won more convincingly, as the Blues kept creating chances: Hrvoje Jukić sent a shot from the left just wide of the post, and Zambata also struck powerfully, but the goalkeeper managed to get to the ball.