The result means Fiji, whose last world championship title came in 2016, leapfrog reigning champion South Africa to lead the overall standings for the first time this year.
Australia seemed to have snatched victory in Singapore after John Porch touched down with 24 seconds left on the clock. But there was time for a reply, and after his side regathered the restart, Alasio Sovita Naduva found his way over to steal it at the death.
It was a pulsating encounter that almost slipped away from Fiji after two quick Australian tries in the closing stages.
"I'm speechless," said Fijian captain Jerry Tuwai.
"Australia are a very good side and took us to the wire. We gave everything for this final.
"To all the people in the stadium, thank you very much for the support and back home thank you very much for your prayers, support and belief in this young team. Winning this tournament will boost our morale going to London and Paris."
'Never write off Fiji'
Fiji's previous triumphs this season have come in Hamilton, Vancouver and Hong Kong, but none were as hard-fought as the final here in Singapore.
After narrow victories over New Zealand and South Africa in the quarters and semis, two tries from Waisea Nacuqu and one from Tuwai put Fiji in control against Australia.
Replies from Brandon Quinn and Porch, however, meant that Naduva's last-gasp score was needed to settle the contest and hand Fiji a third consecutive World Series trophy.
"Awesome final at the Singapore Sevens," tweeted Ben Ryan, who coached Fiji when the Pacific Islanders last won the world championship title.
"Brilliant effort from Australia but never ever write off Fiji if they have the ball with time up."
An entertaining bronze final saw England edge past South Africa 26-24 to equal its best performance of the season so far. USA, meanwhile, claimed the Challenge Trophy after overcoming Canada 26-12.
While Fiji currently leads the overall standings on 145 points, South Africa is hot on its heels on 141 to ensure a tense season finale is in order.
Just two tournaments remain in the 10-stop series, which resumes in London on June 2.