Tries from Peceli Yato and Waisea Nayacalevu helped the Fijians to a 21-12 lead just after the break as a misfiring Australia struggled to turn possession into points and looked to be heading for one of the great World Cup shocks.
However, the Wallabies seemed to sense the danger and suddenly found another gear, with replacement scrumhalf Will Genia driving the pack around the field and using his tactical kicking to force Fiji back into their own half.
That more controlled approach led to hooker Tolu Latu barging over twice in quick succession from driving mauls before Samu Kerevi and Marika Koroibete also went over to take the game away from Fiji.
"It's a testing match for us going down like that. Fiji really came out of the blocks at us, aggressive, they're really big, physical guys, they really took it to us," Australia captain Michael Hooper said.
"Really proud of our guys, to regroup, to work our set piece into the game, and that really paid off for us."
The Fijians had been tipped to be a real threat to the Wallabies with a big and fast pack and an explosive backline and while they promised to be more disciplined and patient it was obvious they wanted to play at pace.
They established an early 8-0 lead through Ben Volavola's first of three penalties and a typical counter-attacking exploitation of space with Yato put over in the corner after winger Josua Tuisova broke two tackles.
After initially trying to match the Fijians with width at pace, Australia's forwards began to build into the game and put pressure on the scrum, with one shunt in the Fijian 22-metre area allowing Hooper to get driven over the tryline.
Volavola, however, managed to extend the lead to 14-7 with two more penalties before Reece Hodge reduced the deficit at halftime to 14-12 when he crossed after the Wallabies created space out wide following an attacking lineout.
Nayacalevu then extended the lead to nine points early in the second half when he pounced on a loose ball in midfield and was mobbed by his team's replacements warming up behind the tryline.
Staring at a possible defeat that could have cost them a place in the knockout phases, the Wallabies went back to basics with the introduction of Genia and big loose forward Lukhan Salakaia-Loto changing the momentum of the game.
They won a succession of penalties inside Fiji's half that led to Latu finishing off driving mauls from attacking lineouts, before simple tries for Kerevi and Koroibete blew the scoreline out.
"It was a disappointing result at the end but I thought we played really well in the first half," Fiji captain Dominiko Waqaniburotu said.
"Just a lot of things we need to work on, like the discipline, which cost us a man in the second half.
"We did a bit well but we need to improve if we want to compete in this competition."
Australia, who also opened their 2015 World Cup campaign by beating Fiji in Cardiff, next play Wales in Tokyo on Sept. 29 while Fiji meet Uruguay on Wednesday.