Fabienne Humm was the star for Switzerland as she needed just five minutes to complete a hat-trick, the fastest one ever recorded.
Switzerland (three points), however, remained three points behind Group C leader Japan (six points) after the Asian team's 2-1 victory over Cameroon.
Aya Sameshima and Yuika Sugasawa scored first-half goals as Japan held off Cameroon's inspired second half activity which included a goal in the 90th minute.
Cameroon also remain at three points for the tournament.
The United States were unable to find a goal in a 0-0 draw with Sweden.
The result kept the suspense alive heading into the final matches in Group D as the U.S., with four, are a point ahead of Australia and two ahead of Sweden.
Sweden controlled much of the first half against the Americans but could not put any real pressure on goalkeeper Hope Solo.
The U.S. subbed in all-time leading scorer Abby Wambach in the 68th minute and she narrowly missed a header opportunity down the stretch.
Earlier in the day, Australia defeated Nigeria 2-0 for their first win of the tournament.
Australia will finish Group D play against Sweden on Tuesday while the Americans close out against Nigeria.
(Writing by Jahmal Corner in Los Angeles; editing by Sudipto Ganguly)
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