Spain needed a late winner against tournament favourites and holders the USSR in front of 80,000 at Madrid's Estadio Santiago Bernabeu, for their solitary cup success on the world stage.
Jesus Maria Pereda fired Spain ahead after just six minutes of the final, but after Galimzian Khusainov equalised just two minutes later Spain had to wait until six minutes from time, Marcelino Martinez heading low into the net.
The hosts had squeezed through a last-16 qualifying tie against Northern Ireland, who held Jose Villalonga's side in Bilbao, before easily beating the Republic of Ireland to reach the final four.
The USSR faced no travel ban as they had four years earlier, winning 3-0 over surprise semi-finalists Denmark - who themselves needed a replay to beat giant-killing Luxembourg in the final qualifying round.
The minnows had beaten Holland over two legs, even though the Dutch had only months earlier beaten world champions Brazil in a friendly.
Hungary, no longer able to call on Ferenc Puskas and many others from the 'Mighty Magyar' side of the 1950s, had forced Spain into extra-time after a later Ferenc Bene equaliser.
But Amancio Amaro, one of the stars of Real Madrid's 'ye-ye' side, scored the decisive goal in front of his home crowd.
The number of entrants rose from 17 to 29, and though West Germany again did not play England and Italy took part for the first time.
But England lost at the first hurdle to France, while Italy were knocked out by the Soviet Union in the second round.
Once again, political wrangling interfered in the tournament when Greece pulled out after they were handed a first qualifying round draw against Albania, with whom they had officially been at war for 50 years.