After New Zealand thumped the Cook Islands 82-16 in Christchurch in Group A, the Australians would have been hoping for an equally emphatic victory over Fiji.
But the Kangaroos had to fight tooth and nail before finally edging a tense encounter, having to twice come from behind.
Fiji won the physical battle throughout, constantly making ground up the middle and out-muscling the home side.
But the Australians took control once their opponents began to tire, sealing the win when Jacob Preston crashed over with three minutes remaining.
Australia captain James Tedesco conceded the Fijians had won the forward battle and said his side made far too many mistakes.
"Credit to Fiji, it was a tough battle in the forwards but I'm proud of the way our boys fought," said Tedesco, whose side are already into the last four of the tournament.
"Our discipline was poor and we made silly errors trying to score with every phase."
Fiji skipper Apisai Koroisau was upbeat despite the loss.
"I'm so proud of what the boys did out there," he said.
"We were just out there enjoying playing and working hard for each other."
In Christchurch, winger Jamayne Isaako scored 38 points as New Zealand overcame a slow start to outclass the Cook Islands.
Isaako scored a hat-trick of tries and converted 13 of New Zealand's 14 tries in a lopsided match.
It was the first win of the tournament for the Kiwis, who opened with a 24-22 loss to holders Australia, while the Cook Islands crashed to a second heavy defeat.
The Kukis scored three early tries, all through winger Esom Ioka, to surprisingly lead 16-12 after the opening 20 minutes.
However it was one-way traffic from that point, with New Zealand pulling 36-16 clear by halftime, slicing through with increasing ease against a defence that became frayed as the match wore on.
Isaako's haul was the second most by a player in a World Cup match, eclipsed by Ryan Girdler's 46 points for Australia in their 110-4 defeat of Russia in 2000.
Kiwi captain James Fisher-Harris said the opening exchanges were tough.
"The Kuki brothers came with that aggression and obviously put some points on the board but we just stuck to what we do best. At the end of it, it was pretty fun," he said.
Cook Islands skipper Kayal Iro said his team struggled to contain opponents stacked with top-flight players from the National Rugby League competition.
"They were just too good for us. I thought we came out hard and obviously Esom had a blinder, but we just couldn't really hold on."
The group concludes next week when New Zealand face Fiji on the Gold Coast and Australia play the Cook Islands in Townsville.
Australia have already reached the semi-finals of the 10-team tournament and will be joined by New Zealand if the Kiwis beat Fiji.
