The Australians thought they had secured victory when they scored off the final kick-off but the referee ruled they had knocked the ball on, giving the flamboyant Fijians a scrum on their own line and one last chance to snatch victory, which they took full advantage of.
The Blitzboks came out firing against and managed to get themselves into the lead, but the Islanders still managed to turn over a 10-point deficit to win 12-10.
Fiji started the match brightly, charging ahead 14-0 after a brace of tries by Waisea Nacuqu, which were complemented by successful conversions.
"We are very harsh when we evaluate ourselves and I am happy that they delivered on those things we wanted. We gave everything for this final", Tuwai said.
"Thank you very much (everyone back home) for all your prayers support and belief in this young team".
Fiji won this season's tournaments in New Zealand, Vancouver and Hong Kong and, with its fourth victory, climbed four points clear of South Africa atop the standings.
"Winning this tournament will boost our morale going to London and Paris".
Sonam Kapoor's house decorated for wedding, guests to receive e-cards soon
This is not the correct time I have had a very good relationship with the media and we will share all in good time. But what's wonderful is to actually work towards the same goal and create the best possible version of something.
Fiji pulled off a stunning win after the final buzzer to claim the Singapore Sevens title and take the overall lead in the series with just two rounds to go.
The penultimate tournament is in London from June 2-3 before the series ends in Paris between June 9-10.
Fiji, who had defeated Commonwealth Games champions New Zealand 24-19 in the quarter-finals before slipping past South Africa in the semis with a 12-10 comeback victory, have a four-point lead over South Africa, who finished fourth in Singapore after losing 26-24 to England in the bronze play-off.
The Kenya Sevens team sailed through to Singapore 7s Main Cup quarter-final after whipping U.S. 33-14 in their last match of Pool B on Saturday.
The All Blacks Sevens have beaten Samoa 36-17 to finish fifth in the Singapore leg of the World Sevens.
It was a tough weekend for the Springbok Sevens squad in Singapore after they dropped to second place behind Fiji in the 2017-18 World Rugby Sevens Series standings, but their coach Neil Powell feels all is not lost.