Two tries from Desiree Miller and Caitlyn Halse had put Australia in the ascendency, after leading 14-5 at half time, but quickfire scores USA's Hope Rogers Erica Jarrell-Searcy put the USA ahead with nine minutes to go.
Loraini Senivutu, Manuqalo Komaitai and Karalaini Naisewa all crossed for Fiji, but a red card for Bitila Tawake denied Cunningham's side a chance to mount an impressive comeback.
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The wing was one of five try-scorers for the world number two side, with McKinley Hunt crossing twice, and Alysha Corrigan, Taylor Perry and Brittany Kassil also scoring.