The Holland international broke the deadlock deep in extra-time with a trademark free-kick past goalkeeper Gianluca Pagliuca.
In their previous two appearances in the final, Barca had lost to Benfica in 1961 and Steaua Bucharest in 1986.
Their team included Pep Guardiola, Michael Laudrup and Hristo Stoichkov, while lining up for Sampdoria were Attilio Lombardo, Roberto Mancini and Gianluca Vialli.
Before Johan Cruyff became coach in 1988, Barcelona had won 10 LaLiga titles but the European Cup had remained elusive.
Since their Wembley victory, they have claimed 16 league titles and four more Champions League triumphs.
The match was the last final before the competition was rebranded as the Champions League the following season.