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.
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.
Lynn replaced Ioan Cunningham as Wales coach earlier this year, and had just three days to prepare his team for the first game of their Six Nations campaign after leading Gloucester-Hartpury to an historic Premiership Women's Rugby treble.
Three hard-working volunteers have been honoured at the Honda Volunteer of the Year awards for their tireless work, effort, and energy at their respective rugby clubs.