Fiji capitalised brilliantly on an ill-disciplined performance from Australia to grab their first win against them since 1954 and jump ahead of the Wallabies in the tightly contested Pool C.
Looking confident from the whistle, Fiji conceded just seven penalties compared to 18 from an Australian side who often looked lost without their injured skipper Will Skelton.
Mastercard Player of the Match Tuisova, when asked about the long gap between victories over Australia, said: "I know it's a long time for us, Fiji, since 19... I don't know, back in the day. It's history for us.
"I just want to thank the boys for their hard work. They gave everything. I just said to them for the second half to empty the tank, give everything they have to try to win this game. We treated this game like a final."
Head coach Simon Raiwalui said: "I'm emotionally drained at the moment. I'm really proud of the boys. It was a great contest, a great Australian side. We're Pacific neighbours so we know each other well. It was a great match. It kept us guessing until the end."
Fiji captain Waisea Nayacalevu admitted his side had treated the game like a final, saying: "What I told the boys today, today is our final. Today will determine whether we want to go up to the quarters so the mindset was do or die, do our best, fight to the end and the result will take care of itself."
Australia now face an important game against Wales on Sunday, 24 September, and Wallabies captain David Porecki said: "They've got world-class players in the backline and they took advantage in and around the breakdown - credit to them. We've got a pretty tight turnaround Wales now, we've got to lick our wounds and get ourselves up for that game, which is easy because it's a World Cup game."
Wallabies head coach Eddie Jones said: "Thoroughly deserved victory for Fiji, they outplayed us, particularly around the ruck. They executed three times more turnovers than us, and in a close game like that, that's the difference."
"For some reason we were just off today. If you look at the stats, we dominated. We scored two tries to one, but we were a poor version of ourselves today, so there's a bit of soul-searching to do, but it makes the Wales game pretty important."