The Americans got off to a slow start, trailing Spain 3-1 after the first quarter before drawing level at 3-3 at the halfway mark. From then on it was all the United States.
"Spain did a good job. We haven't played a match for a while and it just took us a while to get going. The third period was good though and even the second we showed a bit," said U.S. coach Guy Baker. "I hope it was just the fact that we haven't played for a while anyway (the slow start)."
Lauren Wenger scored two goals for the United States, while Natalie Golda, Heather Petri, Alison Gregorka and Kameryn Craig had one each.
Blanca Gil Sorli had all six goals for Spain.
The United States faces its toughest test in Thursday's semifinals when it takes on defending champion Hungary, an 11-9 quarterfinal winner over Canada.
"Our games are pretty similar," Villa said of the Hungarian women. "We are both playing a tight pressing defense and we have both got great shooters. In the end, I think it will come down to the extra player situations."
In other quarterfinals, Russia edged Greece 10-9 and will face the winner of Tuesday's late match between host Australia and Italy, reports AP.
The Australian women will have some extra motivation after their male counterparts lost to Italy in the final seconds of overtime Monday to miss out on a quarterfinals spot.
The import of liquefied natural gas from the United States will not grow, even if Germany exits the Nord Stream-2 project, German Minister of Economy and Energy Peter Altmeier said