Andres Iniesta scored in extra-time to give Spain a 1-0 win and the trophy in South Africa four years ago, and it appeared the same result was on the cards in Salvador when Xabi Alonso powered home a first-half penalty.
But the Netherlands hit back in stunning fashion, with Robin van Persie and Arjen Robben in scintillating form.
Van Persie levelled matters with a fabulous header on the stroke of half-time, before Robben - who fatefully missed a one-on-one with Iker Casillas in the 2010 final - gave Louis van Gaal's side the lead eight minutes after the interval.
Things went from bad to worse for the world champions when Stefan de Vrij nodded home a third on 64 minutes, before Van Persie and Robben netted again to complete a remarkable rout in Group B's opening fixture and cast further doubt over Spain's chances of winning their fourth straight major tournament.
Costa's impact on their system was evident, too, as Spain opted for a more direct approach than in previous tournaments.
It was the Netherlands who created the first opening, Robben's inch-perfect throughball finding Wesley Sneijder, only for the playmaker - making his 100th international appearance - to shoot straight at Casillas.
Costa then spurned a couple of half-openings as Spain began to find their feet and the Netherlands' defending became increasingly desperate.
It was a last-ditch tackle that led to the opener, De Vrij's sliding challenge bringing down the lively Costa - with Alonso coolly converting from the spot.
Van Gaal's side enjoyed a good spell thereafter, but Spain threatened again on the stroke of half-time as Jasper Cillessen kept out David Silva's cute dink following a stunning Iniesta pass.
That miss would become all the more important soon after, Van Persie looping a superb diving header over Casillas after being picked out by Daley Blind's sumptuous long, diagonal ball.
Spain suddenly had no answer to their opponents' new-found verve, Van Persie rattling the crossbar with a vicious strike.
The woodwork could not save Del Bosque's men soon after, though, as De Vrij atoned for his earlier misstep by heading Sniejder's deep free-kick in off the post.
And the Netherlands were not finished there, as Casillas was forced to pick the ball out of the net again as the irresistible Robben took advantage of more lax defending to race clear and round off a scarcely believable result.
