Aberdeen set about their task immediately and battered the well-organised Hungarians from the start. Ujspest were, if nothing else, resilient and were determined to stop the home side at any cost. This included some wild challenges from time to time and Aberdeen did well to remain calm under such provocation. It took the Dons 37 minutes to finally break down the defensive wall and the chance was carved out when McLeish refused to give up the cause and kept in play a ball that looked destined to head for a goal kick.
The second half saw Aberdeen continue to dominate and Black went close with a header before Strachan crashed a free kick off the cross bar with the keeper beaten. It looked as though time would run out for the Dons but Mark McGhee popped up again two minutes from time. A throw in on the left was fed to Neil Simpson and his cross found McGhee in the middle and he prodded the ball past Szendrei from six yards.
The player replacing Szendrei was called into action in the final minute when he dived low to gather a Strachan daisy cutter. The referee then blew for full time and sent the red army home happy and dreaming of a second successive Cup Winners Cup win.