Van Persie pounced in each half as the Dutch recovered from a controversial Xabi Alonso penalty to inflict a crushing defeat on the reigning kings of world and European football.
Stefan De Vrij got the Netherlands' other goal as Spain slumped to the heaviest defeat ever inflicted at a World Cup on the reigning champions.
It was Spain's worst defeat in more than half a century, coming 51 years after a 6-2 defeat to Scotland in 1963.
The extraordinary Group B drama in the northern Brazilian coastal city of Salvador has potentially turned the World Cup permutations on their head.
If Spain fail to recover the form which saw them win back-to-back European titles either side of their 2010 World Cup triumph, they could conceivably crash out in the first round, or face a daunting clash with Brazil in the last 16.
The walloping eclipsed more refereeing controversies on the second day of competition.
FIFA officials earlier defended Japanese referee Yuichi Nishimura after he awarded Brazil a bitterly contested penalty in their opening game victory over Croatia.
"He had a very good position," said Busacca, referring to a photo of the incident which appeared to show Lovren's hands making contact with Fred.
"When he saw the hands doing something he makes it (the decision)."
But no sooner had referees chief Busacca sprung to Nishimura's defence then the standard of officiating was again under scrutiny as Mexico took on Cameroon.