Spain's thrilling victory at Eden Park sets up a showdown in Sydney on Sunday with either Australia or England, who meet in the other semi-final on Wednesday.
The semi-final in Auckland seemed to be drifting towards extra time before suddenly bursting to life when substitute Salma Paralluelo put Spain ahead with nine minutes left.
Rebecka Blomqvist equalised for Sweden in the 88th minute only for full-back Carmona, Spain's captain, to score with a superb shot in off the underside of the crossbar from the edge of the box.
It has been a remarkable run for a nation who had never previously gone beyond the last 16 at a Women's World Cup, and for a team who had been in disarray in the months leading up to the tournament.
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