Goals to Americans Maggie Steffens and Kami Craig in extra time were enough to get past the brave Australians, who fought back dramatically to level the game 9-9 in the final second of regulation time.
Ash Southern scored four goals for Australia, including the match-levelling penalty shot.
The heated rivalry between the two teams, consistently the best two female sides in the world since the women's game was introduced as an Olympic event in 2000, was clearly on show.
The Stingers will now face either Spain or Great Britain in the play-off for bronze.
More to follow.