Australia has beaten Fiji 28-13 in Cardiff, but failed to secure a bonus point after dominating their opening Rugby World Cup Pool A match.
Fiji have now lost both of their games.
Number eight David Pocock claimed two tries from rolling mauls in the first half to lay the platform for the two-time world champions, with a try to prop Sekope Kepu soon after the interval setting them on course for a comfortable win.
But Fiji rallied through a try by flyhalf Ben Volavola and an inexplicable decision by Australia to kick a penalty 10 minutes from time rather than go for a fourth try, leaving the Wallabies a point behind England and Wales in the group.
The teams exchanged early penalties, before livewire Fiji scrumhalf Nikola Matawalu made a sniping break, but desperate Australian defence prevented a try and the Wallabies broke back downfield.
They rejected the chance to kick a penalty and from the resulting lineout Australia formed a rolling maul, Pocock touching down after 27 minutes.
Fiji prop Campese Ma'afu was sent to the sin-bin for kicking the ball away and the Wallabies immediately took advantage when Pocock grabbed his second try in identical fashion.
Australia led 18-3 at halftime and soon extended the advantage.
Fullback Israel Folau made an incisive break, and with the Fiji defence in disarray, Kepu showed neat footwork to get over the line.
Fiji, who lost their opening Pool A match 35-11 to England five days ago, looked jaded, but they roused themselves impressively.
Volavola jinked his way past three defenders and had sufficient strength to force his way over the line to make the score 25-13.
Fiji tried to stretch the defence with some expansive rugby, but tireless Australian flanker Michael Hooper made a succession of tackles to keep them out.
Australia flyhalf Bernard Foley kicked another penalty to extend the lead, but with centre Tevita Kuridrani in the sin-bin, the Wallabies did not have the energy to cross for the fourth try.
That could be costly in the tournament's toughest group, in which England play Wales on Sunday.
"It was a really good work-out for us, very physical," said Australia coach Michael Cheika.
"It was exactly what we needed and I was pleased with a lot of the things we did.
"We'll turn the team around now for Uruguay on Monday."