On Friday, they beat France in the quarter-finals before falling to New Zealand in the semis.
But a flawed tactical decision to use a grubber kick to the corner in the last seconds led to a knock on and Fiji showed skill and patience to create a length-of-the-field try.
After narrowly missing out on a place in the Cup quarter finals on day one, England thrashed Papua New Guinea 52-0 in the semi-final.
For the first time, Australia's women's rugby sevens team will wake up just one win away from a World Series title.
The nail-biting victory made it three from three for Australia at Allianz Stadium after earlier wins against Canada (27-5) and U.S. (26-19).More news: Padmaavat box-office collection Day 2: Sanjay Leela Bhansali's film exceeds expectations
Tom Lucas scored with less than a minute remaining to give Australia the vital win after Scotland had gone ahead 21-17 with Max McFarland's try only minutes earlier.
"Every time we play Fiji it seems to be like that".
New Zealand, winners of the last World Series leg in Cape Town last month, were edged-out in a thrilling Group A clash with Fiji in which they led 17-14 before conceding a try with the last play of the game to lose 19-17.
Russian Federation beat the United States 19-14 and Canada beat France 28-12 in other quarterfinals.
Emilee Cherry then propped, stepped and accelerated down the left wing to outsmart the Spanish defence and score Australia's second.More news: Gronkowski listed as DNP with concussion
Seven members of the Canadian roster are holdovers from the bronze-winning side at the 2016 Rio Olympics.
Australia and New Zealand have been battling it out for Sevens supremacy and they'll have another showdown in Sydney on Sunday afternoon.
"Player for player they're really good match-ups", he said. "Here in Sydney we are focused on the basics because we know we can punish teams if we play to our game plan".
Up 26-0 at halftime, the All Blacks Sevens lifted another notch by scoring five second-half tries to record the biggest win of the opening day.More news: Ronald Gasser Convicted of Manslaughter in Fatal Shooting of Joe McKnight