Captain Michael Hooper and winger Reece Hodge had already crossed for Australia in the first half, but the 1991 and '99 World Cup winner didn't really have control until the final 30 minutes.
Then, Australia tightened up and exposed Fiji's maul to send Latu over twice in the space of five minutes.
Backs Samu Kerevi and Marika Koroibete, both born in Fiji, scored late to make it appear comfortable for Australia, which scored six tries in all and averted what would have been its most surprising defeat at a World Cup.
Australia hasn't lost to Fiji since 1954 and has only lost two pool games in its Rugby World Cup history. It has made the quarterfinals at every World Cup.
That pool-stage record was in major danger when Fiji winger Josua Tuisova rampaged down the right wing in the early exchanges, bursting through one tackle and fending off another, to set up the try for flanker Yato.
That score added to a penalty by flyhalf Ben Volavola and gave Fiji a surprise 8-0 lead at the Sapporo Dome.
Australia recovered momentarily when Hooper drove over in the 18th and Christian Leali'ifano converted for 8-7.
Volavola kicked two more penalties but Hodge added a second try for Australia five minutes before halftime.
Fiji's powerful runners were bursting through tackles and knocking the Australians defense, and Australia was making error after error under the pressure.
Although the momentum appeared to start shifting toward Australia by the end of the first half, Nayacalevu's try two minutes into the second lifted Fiji again.
He scooped up a dropped pass by Leali'ifano, pushed the flyhalf away, and scampered half the length of the field to score between the posts.
Australia found more success in the tight exchanges and the rolling mauls, when Latu scored both his tries in the right corner, and took control of the game when Fiji had a player in the sin-bin late in the second half.
Those gave the Wallabies enough breathing space to spread the ball a little wider, setting up late tries for center Kerevi and wing Koroibete.
- AP
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