Frappert was advised to review by VAR and ruled that there was not enough contact with Paredes, who had his yellow card withdrawn, much to the animated displeasure of Berenstein.
Spain went ahead with nine minutes of normal time through Caldenti after Van der Graagt fumbled on Parluelo’s cross inside the penalty box.
Inter Milan defender Van der Gragt made amends in the first minute of stoppage time when her surging run was found by Viktoria Pelova before volleying Kata Cole inside the far post.
The Netherlands had the better chances in extra time, going close twice through Berenstein before conceding the decisive goal from Barcelona forward Parluelo.
World Player of the Year Alexia Puteles, who is recovering from a knee injury, was substituted off the Spanish bench during extra time.
However, they would have to play without defender Oihen Hernandez in the semi-finals after he was shown a yellow card for a foul.