Nathalie Bjorn sent a hanging cross over the back post from the right for Fridolina Rolfo – who was facing seven of her Barcelona club-mates in Spain’s starting line-up – but her side-footed volley was saved by Cata Cole took.
Vilda’s plan was clearly to save the speedy Paraluello when the Swedish defense began to tire, and it was just before the hour mark that he turned to the former athlete.
Parluelo replaced Putelas, who is yet to complete 90 minutes at this World Cup as he recovers from a serious knee injury.
The substitute’s persistence brought the opener for Spain with almost 20 minutes remaining as she moved to put the ball in play after Hermoso’s cross, but Alba Redondo fired wide of her cutback.
Then with nine minutes of normal time remaining, Parluelo showed killer instincts and fired a low shot into the corner.
But Sweden did not give up and got the equalizer in the 88th minute thanks to two of their substitute players.
Lena Hurtig had just come on when she headed in a cross for Blomqvist to score, once again leading to extra time.
But Real Madrid left-back Carmona had other ideas as he led Spain to victory in spectacular fashion.