He started the World Cup as a substitute, but played in Denmark's last two matches at the tournament. Høgh replaced Troels Rasmussen as starting goalkeeper when Denmark beat Germany 2-0 and advanced to the knock-off stage. In the round of 16 against Spain, Høgh conceded four goals to Spanish striker Emilio Butragueño, as Denmark lost 5-1 and was eliminated from the tournament. After the 1986 World Cup, Høgh was named 1986 "Best Goalkeeper of the Year". Troels Rasmussen reclaimed his starting position in the national team, and Høgh played what would be his last national team in eight years in September 1987. With the emergence of record-setting goalkeeper Peter Schmeichel, Høgh established himself as one of Schmeichel's most frequent understudies.