They've piled on 210 points in their past four games and haven't conceded a single try.
Hayne continued his remarkable form in the centres, taking his tournament try-scoring tally to nine, while winger Darius Boyd had a double.
Man-of-the-match Johnathan Thurston and fellow playmaker Cooper Cronk ran riot while Greg Inglis, starting at fullback in place of the injured Billy Slater, was his usual dangerous self and Paul Gallen did the most damage up front.
The Kangaroos stormed to a 34-0 lead at halftime, running in six first-half tries.
Fiji started solidly but could only hold out the favourites for nine minutes with Thurston scoring with a fairly soft try.
Boyd crossed out wide in the 15th minute before Hayne set up Cronk four minutes later with a brilliant inside ball from the sideline.
Hayne got his first try four minutes later after being set up by Inglis, Josh Papalii barged through under the posts before Hayne added a second on the stroke of halftime.
After a slow start to the second half, James Tamou kept things ticking over when he stretched out to score in the 54th minute before Boyd crossed for his second.
Hayne scored his third in the 68th minute and could have had a fourth soon after but he unselfishly set up winger Brett Morris and Andrew Fifita completed the rout with a late try under the posts.
Saturday's match brought an end to the illustrious rugby league career of Fiji captain Petero Civoniceva, who played 35 Tests for the Kangaroos.
In the earlier game, England - led by the superb Sam Burgess - looked set to book an unlikely final berth before Shaun Johnson's last-minute try and conversion got New Zealand out of jail.
