Meninga made eight changes from the 84-0 win over Scotland last week, and gave wing Josh Addo-Carr a rest against the Italians after his six-try showing over the two previous group games.
Meanwhile, England lashed Greece 94-4 in Sheffield and Fiji beat Scotland 30-14 in Newcastle.
Cherry-Evans launched the Kangaroos with a chip caught by Valentine Holmes for a try in the corner. Centre Murray Taulagi scored five minutes later, followed by captain James Tedesco against the Italian side he played for at the previous two World Cups.
Winger Campbell Graham was gifted a try by Italy, then Latrell Mitchell scored one and produced an audacious backhand offload for Taulagi’s second. They led 30-0 at halftime.
Tedesco was spelled after their seventh try, and the biggest cheer came about an hour in for Italy when forward Ronny Palumbo pounced on a grubber kick to score their only try.
The Australians replied with four more tries.
Winger Dom Young scored a record-tying four tries for England, all in the first half. He leads the tournament list with eight in three matches.
England notched 17 tries against Greece by 11 different players. Marc Sneyd kicked 13 goals and contributed 30 points.
Sneyd also had a hand in several tries, and scored one of his own after halftime, when England led 44-4.
England swept Group A and face a quarter-final next weekend against the runner-up in Group D, probably Papua New Guinea.
By fulltime at Bramall Lane, England posted the second highest score in World Cup history, second only to Australia beating Russia 110-4 in 2000.
“It was an awkward one to deal with,” England coach Shaun Wane said. “The record doesn’t interest me, I was looking for habits and certain things that will help us beat Papua New Guinea if we get them.”
Greece were eliminated without a win at their first World Cup but were heartily cheered while they lapped the field after the match.
Fiji were grateful for being tested by Scotland, ahead of a quarter-final matchup with New Zealand.
“We needed it,” interim coach Wise Kativerata said. “We needed to work on our attack because we’ve been working hard on our defence.”
Fiji scored five tries to Scotland’s three. All five were converted by Brandon Wakeham.
The Fijians led 18-8 at the break and 24-14 with 30 minutes to go, and finally made the result certain when sustained pressure led to a Korbin Sims converted try while the teams were playing 12 on 12. Fiji second rower Viliame Kikau and Scotland winger Lachlan Walmsley were occupying the sin-bin.
Scotland bowed out after three group losses, while Fiji will take consecutive wins into the showdown with the Kiwis next weekend.
“We’ve got the team to play New Zealand,” Kativerata said. “We’ve got the younger squad, so when we play our style of football our energy goes up, everything goes up.”
