Over a tense 90 minutes in Wellington full of incident, Mariona Caldentey scored an 81st-minute penalty for Spain, only for Dutch defender Stefanie van der Gragt to equalise in added time 10 minutes later.
With the quarter-final seemingly headed for penalties, the 19-year-old substitute Paralluelo produced a brilliant solo finish in the 111th minute to put Spain into the last four for the first time.
They will now face Sweden or Japan in Auckland on Tuesday while the tournament is over for the Dutch, beaten finalists four years ago. "It's hard now," said Van der Gragt, whose last game in football was an eventful one -- conceding the penalty for handball, then equalising, before Paralluelo's decisive, late intervention. "We had the chance in extra time and we didn't score, they had one chance and they scored.
That's football." It was reward for a display of controlled attacking football from the sixth-ranked La Roja, who have regained their swagger after crashing to a 4-0 group-stage loss to Japan.