The Dutch avenged their defeat by the same opponents in the 2010 final in outrageous style, with four unanswered goals in an irresistible second-half display in Salvador.
Van Persie and Robben scored two apiece, with each man's first a minor classic in its own right. Defender Stefan de Vrij scored his side's third.
Vicente Del Bosque's side, who also lost their opener against Switzerland four years ago, had actually taken the lead through Xabi Alonso's disputed penalty, a lead they held until Van Persie's instinctive flying header levelled matters just before the break.
After that, the Netherlands were rampant, laying a big marker down for the remainder of the tournament and raising the prospect of a Brazil-Spain second-round tie.
In the beginning, the Dutch were being dictated to by Xavi, Andres Iniesta, David Silva and Xabi Alonso, with Ron Vlaar producing at least two desperate blocks.
The controversial penalty followed in the 26th minute, starting with Xavi's beautifully weighted pass for Costa. He surged into the area and took two touches before turning De Vrij, who appeared in real time to trip him. By the time Xabi Alonso had buried the spot-kick, replays showed Costa apparently initiating contact.
Van Persie levelled, reading the space perfectly as he leapt to head Daley Blind's hanging cross high over the helpless Casillas, before a piece of Robben magic gave them a second-half lead. Van Persie's chip picked out his team-mate, but he had plenty still to do as he controlled the ball brilliantly with the outside of his boot before turning Gerard Pique and Sergio Ramos, converting with a slight deflection off the latter.
There was no holding them back now, De Vrij making it 3-1 from Sneijder's curling free-kick.
And the pace only increased, Silva's close-range finish chalked off for offside before the Netherlands extended their lead to three.
Casillas was wholly culpable this time, turning a harmless back pass into one dreadful touch and an open goal for the alert Van Persie.
Robben completed Spain's misery with 10 minutes to go, collecting Sneijder's pass and then reducing Casillas and his defenders to a floundering mess as he made room for an emphatic finish.
They might have scored more, towards the end. They had already made a hell of a statement.