The victory was the Faroe Islands' first in history in a women's World Cup.
Goalkeeper Rakul Wardum made 15 saves and Pernille Brandenborg scored seven goals, two of which were penalties, on as many shots.
The Faroe Islands lost their opening match against Montenegro on Wednesday, but will advance with a victory against pointless Paraguay on Sunday and take the points from the Spain match with them.
This is the second major sporting success for the Faroe Islands in a short time. Earlier this fall, the men's national football team defeated the Czech Republic 2–1 in a World Cup qualifying match.
