With 70 minutes gone of Schalke's first European final, Wilmots picked up the ball in the middle of the Internazionale half, took a few strides forward and fired the ball low into the left-hand corner.
Apart from that piece of brilliance by the Belgian international, Schalke, who dominated German football in the Thirties and early Forties, did not create a single scoring chance in a match which rarely rose above the mediocre.
Inter, who won this trophy in 1991 and 1994, were without Paul Ince and the Frenchmen, Jocelyn Angloma and Youri Djorkaeff, because of suspension and struggled to get their game together. "It wouldn't be the first time that a team has lost away from home and then turned the result around," Inter's English coach, Roy Hodgson, said.
Apart from long-range shots from Ingo Anderbrugge and Olaf Thon, Schalke hardly threatened the Italians' goal in the first half. Inter's best chance came just before the interval when Maurizio Ganz broke free on the left but Jens Lehmann touched his shot over the bar.
Inter's sweeper, Fabio Galante, was booked and misses the game in Milan in two weeks' time.
Schalke 04: Lehmann; Thon, Kock, Linke, Latal, Eigenrauch, Muller, Nemec, Buskens (Max, 68), Anderbrugge, Wilmots.
Internazionale: Pagliuca; Bergomi, Galante, Paganin, Pistone, Zanetti, Sforza, Fresi (Berti, 60), Winter, Ganz, Zamorano.
Referee: M Batta (Fr).