The Costa Rican striker further endorsed Hammers' close-season gamble of entering the Intertoto Cup as he earned the London club's place in a two-legged final game against the French side Metz.
Their manager Harry Redknapp had feared that his players would be distracted by thoughts of Saturday's opening Premiership game at home to Tottenham, but Wanchope's goal doubled their aggregate lead over Heerenveen to ease the pressure.
Wanchope's goal, his first for the club since his pounds 3.5m move from Derby, came at a time when the Dutch side were beginning to control the game. John Moncur played a short corner for Frank Lampard to hit a 30-yard shot which the Heerenveen goalkeeper, Hans Vonk, failed to hold. Wanchope reacted quickly and drove the loose ball into the top left-hand corner from close range.
West Ham could have taken the lead after only four minutes when Trevor Sinclair played the ball into the penalty area and the Italian striker Paolo Di Canio dummied to set up Wanchope, but he dragged his shot just wide.
West Ham did not have it all their way as Heerenveen managed to get six of their eight first-half shots on target to demand the best from the West Ham goalkeeper, Shaka Hislop.
The Hammers pressed forward and on 55 minutes Wanchope's clever ball found Sinclair unmarked, but his right-footer was pushed to safety.
Heerenveen: Vonk, Hansma, Mitrita, De Nooijer, Talan (Hakansson, 76), Denneboom (Lurling, 60), Samardzic, Pahlplatz, Nurmenta, Huizingh, Venema (Radomski, h-t). Substitutes not used: Ditewig, Pander, Jensen, Holm.
West Ham: Hislop, Lomas, Pearce, Ferdinand, Minto, Sinclair, Lampard, Foe, Moncur (Cole, 83), Wanchope, Di Canio (Kitson, 73). Substitutes not used: Forrest, Potts, Carrick, Wright, Keller.
Referee: P Garibian (France).