For the first time it was extra time that settled the Welsh Cup final after the sides had been level at 9-9 after 80 minutes play.
A crowd of 37,500 were at the National Ground in Cardiff to watch the home club, led by hooker Alan Phillips, (now team manager of Wales), lead 9-3 at the interval with a hat-trick of penalties by fly half Geraint John.
Swansea came back and fly half Tony Clement dropped a goal, before international full back Mark Wyatt kicked his second, and equalising penalty. The All-White were driven on by skipper Richard Moriarty and his younger brother Paul in their pack.
But, Cardiff were to make it a third win in four seasons and fifth in seven seasons as wing Gerald Cordle scored in the corner and full back Michael Rayer landed a 35-yard drop goal. Swansea made one last break and centre Kevin Hopkins scored for Wyatt to convert, but it was just too late for them.
England international centre Richard Cardus was an injury-time replacement for Mark Ring in the Cardiff backs.
Swansea players Clement and Paul Moriarty are now Swansea coaches, while prop David Young is now the Cardiff coach.
Cardiff had beaten Welsh club champions Neath by 16-6 in a semi-final at Neath and Swansea gained a 20-3 success in the other semi over Newbridge at the Cardiff club ground.
Teams in the final were: -
Cardiff - M Rayer; G Cordle, A Donovan, M Ring (R Cardus), A Hadley; G John, C Hutchings;J Whitefoot, A Phillips (capt), I Eidman, H Stone, R Norster, R Lakin, J Scott, G Roberts (T Crothers).
Swansea - M Wyatt; M Titley, K Hopkins, M Dacey, A Emyr; A Clement, Robert Jones;Keith Colclough, P Hitchins, David Young, Maurice Colclough (J Williams), R Moriarty (capt, P Moriarty, J Thomas, R Webster.
Referee: Winston Jones (Ammanford).