Despite leading Fiji 15-5 with less than five minutes to play, Australia blew the 10-point lead by conceding two late tries and then failing to capitalise on a golden chance after the siren.
It is the third time Australia have suffered a late capitulation to the world champions this year, after they threw away a 15-0 lead in the second half of the final in Las Vegas, and also squandered a nine-point lead in the final 90 seconds against the same team in the quarter-final in Singapore.
"I thought we had the game to beat Fiji, but we really need to be finishing those types of games," coach Andy Friend said.
"I keep saying it, but I truly believe we are getting closer to them."
The Thunderbolts went on to lose to South Africa in the Plate Final to finish sixth, while Fiji were stunned by a fast-finishing Samoan side in the final, losing 29-26 after leading 26-7.
Of more concern to Australia though will be their continual habit of throwing away sizeable leads just three months away from the Olympics.
They also lost possession and the lead in the final seconds of the Sydney Sevens final against New Zealand in February, and conceded 12 late points against the same opponent in the pool stage of the tournament to draw.
One player now likely to appear at the Olympics is Jesse Parahi, who impressed in his first Sevens tournament in Paris on return from rugby league.
"He was a big positive. Jesse's like a bull and carried the ball so well when we needed it," Friend said.
Meanwhile Wallaby Nick Cummins was given little time in the big matches, while Con Foley threw his hands up to be James Stannard's halves partner if regular five-eighth Lewis Holland fails to overcome an ankle injury.