The Dutch fell behind to Xabi Alonso's penalty midway through the first half in Salvador, but drew level shortly before the break when Van Persie acrobatically headed in Daley Blind's lofted pass.
The second half was all Netherlands, as Louis van Gaal's men put in a devastating attacking display to stun the reigning champions and take an early grip on Group B.
Arjen Robben and Stefan de Vrij put Netherlands 3-1 in front, before both Van Persie and Robben doubled their tally as Spain crumbled.
"This is inexplicable," Van Persie told NOS. "We have trained all those weeks for this.
"The match has gone exactly as the coaching staff predicted.
"That (first) goal came at a good time. Our second goal then came as a blow to Spain.
"After that we continued. Often, you quit after two or three goals. But we went on, and on, and on."
Van Gaal hailed the importance of his striker's equalising goal, explaining that it allowed him to hold off making a tactical switch at half-time.
"If Van Persie wouldn't have scored the 1-1 before half-time, I would've switched back to the 4-3-3 formation," he said.
"If I played with three attackers, my wingers would have chased down the Spain backs too much, that would be a waste.
"I played this system because I believe that we are not good enough to beat Spain with our normal 4-3-3 formation.
"We still have to beat Australia to make this victory count."
