The French side produced a display of technical flair which was too good for the outclassed Austrians, and Bruno N'Gotty rewarded their dominance with the vital goal in the 29th minute. The defender collected a free- kick from Djorkaeff and unleashed a low 30-yard drive that sped beyond the reach of Rapid's goalkeeper, Michael Konsel, with the aid of a slight deflection.
The Parisians, the pre-match favourites after they had beaten Celtic, Parma and Deportivo La Coruna on the way to the final, found the net again shortly before the end, but Patrice Loko's close-range effort was ruled offside.
Loko's failed opportunity was just one of a series of clear chances for PSG, who dominated throughout and should have sealed the issue well before the break.
Loko, Djorkaeff and Julio Dely Valdes, a first-half substitute for the injured Brazilian, Rai, had a string of chances but either blew them or saw them stopped by Konsel, the overworked Rapid goalkeeper.
Rapid had little to offer and threatened only in the dying minutes through their prolific striker, Carsten Jancker, and the Bulgarian international, Trifon Ivanov.
Luis Fernandez, the PSG coach, who will step down this summer, said: "We played the match we had to play and we got better as the game went on."
PSG, who have flopped in the semi-finals of all three European club trophies in the last three seasons, became only the second French club to win a European trophy, after Marseille's tainted success in the 1993 Champions' Cup.
The Austrians, always second best last night, have tasted defeat in the competition before, in 1985, when they crashed 3-1 to Everton. Last night saw the first major final played at the former Heysel stadium since that year's European Cup final between Juventus and Liverpool, which led to the deaths of 39 people. About 250 fans were detained before last night's game, but there was no violence inside the ground.
Paris St-Germain: Lama; Fournier (Llacer, 78), N'Gotty, Roche, Le Guen, Colleter, Bravo, Guerin, Djorkaeff, Rai (Dely Valdes, 14), Loko.
Rapid Vienna: Konsel; Hatz, Guggi, Ivanov, Schottel, Stoger, Stumpf (Barisic, 46), Marasek, Jancker, Kuhbauer, Heraf.
Referee: P Pairetto (Italy).Reuse content