A resplendent first 45 minutes from La Celeste saw them open up a 2-0 lead, with Luis Suarez’s free-kick and Diego Laxalt’s deflected strike putting them in the driving seat.
Igor Smolnikov’s red card threatened to see the South Americans run away with it, but the hosts stood strong before a late Edinson Cavani goal put gloss on the victory.
They must also hope France do them a favour by beating Denmark in the other match at the Luzhniki Stadium in Moscow.
Here’s our talking points ahead of the game.
What’s up with Tim Cahill?
The non-appearance of the Socceroos legend has been difficult to understand so far at this World Cup.
Australia have been desperate to find goals in both their games to date – one to save a point against France in the opener and one to get a much needed victory over Denmark.
But despite this, and having the Socceroos record goal scorer at his disposal on the bench, coach Bert van Marwijk has been reticent to introduce Cahill.
Instead making the curious decision to throw on Jackson Irvine, the Hull Midfielder not known for his goal scoring exploits.
But now the perfect opportunity has arisen with starting striker Andrew Nabbout injuring his shoulder during the Denmark match and being ruled out of the crucial Peru clash.
Tomi Juric will come into the starting line-up in place of Nabbout but surely the door must now be open for Cahill to come on as a substitute.
A late winner would be the perfect fairy tale ending for Cahill and allow him to become just the fifth player to score in four World Cups, joining Pele, Uwe Seeler, Miroslav Klose and Cristiano Ronaldo.
BREAKING: Jefferson Farfan suffered a "traumatic brain injury” in training and will miss Peru’s match vs. Australia pic.twitter.com/72OHcVuEbl— B/R Football (@brfootball) June 25, 2018
No Farfan for the Incas
Peru also have their injury issues upfront with Jefferson Farfan ruled out as he remains in hospital after being knocked out in training at the weekend.
Coach Ricardo Gareca admits the team suffered a “scare” when the Lokomotiv Moscow striker collided with a team-mate on Saturday, with the Peruvian Football Federation confirming he has sustained a “traumatic brain injury”.
Concussion protocols mean the 33-year-old will miss Peru’s last match before they fly home having already been eliminated after their first two fixtures.
Australia must score from open play
It’s a long time since Australia scored a goal in open play at the World Cup – way back to Brazil in 2014 when Tim Cahill knocked one in against the Netherlands in the 21st minute of their clash at Estádio Beira-Rio.
The second goal in that match came from the penalty spot courtesy of Captain Courageous Mile Jedinak, who has also scored both of Australia’s goals so far in this World Cup – also from the spot.
Australia have looked industrious in their two matches so far, with Mathew Leckie especially busy around the box.
But neither Celtic’s Tom Rogic or the injured Nabbout really looked like scoring against either France or Denmark and that has to change if Australia are to get the much needed victory against Peru.
The Incas attack has also been poor as they have failed to get on the score sheet at all so far in the tournament – either from the penalty spot or open play. And with Farfan out injured, scoring becomes even tougher for the South Americans.
With Peru’s lack of threat upfront and the Socceroos regent need to score goals to progress, surely Van Marwijk must now relax his safety first approach and go for broke.
Or rely on VAR and the ice-cool nerves of Mile Jedinak.
Australia’s potential progress to the World Cup knockout stage could cost goalkeeper Mathew Ryan financially but he will be more than happy to bear the burden.
The Brighton star has paid for 27 family members to come and watch him in Russia and he insists they have no intention of heading home early.
The Socceroos have to beat eliminated Peru in Sochi and hope already-qualified France defeat Denmark, currently second in Group C.
“I guess that’s the influence family have on you,” said the 26-year-old, whose extended family group ranges from a three-year-old cousin to his 70-something grandfather.
“They have been there along for the journey since I was born with my mother, they’ve witnessed every sacrifice and everything I’ve had to go through.
“It’s the first time, other than my mother and sister, I’ve paid for the family to come across and watch but the chance to share something like this with them was a no-brainer.
“Half of them said yes, half of them are still at home – which is a little bit better for the bank account I guess.
“Fortunately the life I lead now enables me now to try to give back to them but to share an experience like this with them is going to be something I will remember for the rest of my life.
“I hope they do too for the right reasons. Their plan is not to leave and ours isn’t either.”
Peru coach Ricardo Gareca insists he is not thinking about his future ahead of their final match while 34-year-old captain Paolo Guerrero has not ruled out being around for qualifying for Qatar 2022.
“We know once this is over we have to start thinking about the future but right now we are thinking about the match tomorrow,” said Gareca, who will be without striker Jefferson Farfan after he was admitted to hospital with concussion after a training-ground accident.
“Once this World Cup is over I will have to take a decision. The whole country wants an answer, the national team wants an answer.
“I understand it is reasonable I give a swift response but I can’t really tell you when that will happen. I have to make a decision soon.”
Guerrero – who had a 14-month suspension after testing positive for cocaine, which he maintains came from contaminated tea, temporarily lifted two weeks before the tournament – is hopeful of extending his international career.
“I don’t know if this will be the last match for me at a World Cup. I feel I can still contribute and play in the future,” he said.
“I don’t know how long the suspension will last. I will keep fighting for my career.”
Gareca admits the team suffered a scare when Lokomotiv Moscow striker Farfan was hospitalised with a “traumatic brain injury”.
“We were very concerned. He was unconscious for a couple of minutes,” he added.
“Unfortunately he cannot play tomorrow but the most important thing is he is recovering and will get well.”