The United States finished with the silver medal in Beijing and Hungary finished fourth. The victory Monday gave the Americans a large boost in their bid won win a gold medal for the first time since women began playing the sport in the Olympics 12 years ago.
Although Villa did most of the scoring, Courtney Mathewson produced the final three United States goals over the last 7 minutes.
She scored with 1:51 remaining to give the Americans a two-goal lead.
In the other Group A game, Spain defeated China 11-6. The United States and Spain will meet in their group game Wednesday.
Group B action saw Russia edge Britain 7-6 and Australia defeat Italy 10-8.
The Netherlands, which did not make it to this year's tournament, downed the United States 9-8 in the 2008 finals.
The top two finishers in each of the four-team groups will advance to the semifinals.