The first leg in Germany ended in a 0-0 draw and goals from Neil Simpson and Mark McGhee earned Alex Ferguson's side victory in the return.
It was Aberdeen's second European trophy following their triumph against Real Madrid in the Cup Winners' Cup final in Gothenburg.
Aberdeen's winning team
1 Jim Leighton
2 Stewart McKimmie
3 John McMaster
4 Neil Simpson
5 Alex McLeish
6 Willie Miller
7 Gordon Strachan
8 John Hewitt (Eric Black 65)
9 Mark McGhee
10 Dougie Bell
11 Peter Weir
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