Match ends, Australia 0, Peru 2.
Peru recorded their first win at a World Cup finals since 1978 as they beat Australia in the last match of the tournament for both sides.
Australia needed to defeat already-eliminated Peru and hope France beat Denmark in order to reach the last 16, but the South Americans went ahead with a fine, low 15-yard volley from Andre Carrillo.
Excellent defending from Anderson Santamaria denied Mathew Leckie a close-range equaliser as Australia struggled to create clear-cut chances.
Peru captain Paolo Guerrero, only able to play in the tournament after a tribunal overturned a 14-month drug ban, sealed the victory when he spun and shot into the far corner.
Christian Cueva also hit a post for Peru late on as they finished third in Group C above Australia, while France qualified as group winners after their goalless draw with Denmark.
Peru had played eight World Cup finals matches without a win since they beat Iran 4-1 on 11 June, 1978, and this victory was only the fifth in their history.
- Relive Australia v Peru as it happened
- Who needs what? Remaining group permutations
- France top Group C after draw with Denmark
Guerrero scores World Cup goal after overturned ban
Peru were playing in their first world Cup tournament since 1982, although their qualification had been fortunate as they had lost 2-0 against Bolivia in qualifying, but that result was given as a 3-0 Peru win as the Bolivians fielded Paraguay-born Nelson Cabrera as a late substitute.
Nevertheless, more than 40,000 Peruvians travelled to Russia and they have been determined to enjoy every moment.
Once again their fans made for a terrific atmosphere in Sochi, even though 1-0 defeats to both Denmark and France in their opening two games meant they had no chance of progressing.
It only took 18 minutes for the South Americans to take the lead when Carrillo, who spent the 2017-18 season on loan at Watford from Benfica, connected perfectly with Guerrero's cross for their first goal of the competition.
Their second came just five minutes after the break when Peru's record goalscorer Guerrero doubled his side's lead.
The 34-year-old had been set to miss the World Cup having been given a 14-month ban after testing positive for cocaine, although Guerrero has always maintained his positive test in October 2017 came after drinking contaminated herbal tea.
His ban was overturned just before the start of the tournament after the captains of group rivals Australia, Denmark and France wrote to Fifa asking them to lift the ban.
It was a fully deserved result for Guerrero and his team to give his country's supporters the win they desired.
No goal at a fourth World Cup for Cahill
For Australia it was a disappointing way to bow out of the competition and they have now only won twice in 16 matches at World Cup finals.
Mile Jedinak, who had scored both of their goals from the penalty spot in Russia, shot well over the top early on before Peru scored their first.
Peru defender Santamaria did excellently to produce a goal-saving challenge at the near post to deny Leckie after Robbie Kruse's low cross had beaten goalkeeper Pedro Gallese.
Not even the second-half introduction of ex-Everton forward Tim Cahill could give Australia a way back into the game.
The 38-year-old, who had not featured in Australia's opening two games, was aiming to become only the fifth man in World Cup history to score in four World Cups after Brazil's Pele, German duo Uwe Seeler and Miroslav Klose, and Portugal's Cristiano Ronaldo.
However, Cahill did not have a chance, although he could have been picked out by Aziz Behich, who decided to shoot instead and pulled his effort well off target.
Man of the match - Andre Carrillo (Peru)
Australia go home without a win, again - the stats
- Australia failed to win a match at a World Cup tournament for the third time in their five participations (1974, 2014 and 2018).
- Peru won their first match at the World Cup since a 4-1 win over Iran in 1978 - 14,625 days ago.
- Peru forward Pablo Guerrero - aged 34 years and 176 days - became the third oldest South American scorer at the World Cup, behind only Argentina's Martin Palermo (36 years, 227 days) and Obdulio Varela of Uruguay (36 years 279 days).
- Peru's opening goal in this match was their first at the 2018 World Cup from their 28th shot of the competition.
- Australia's first two used substitutes in this match - Tim Cahill (38 years) and Daniel Arzani (19) - are separated in age by 19 years and 29 days.
- Peru opened the scoring in this match, only the third time they have done so in 18 World Cup matches and the first time since 1978 against Iran.
- Tim Cahill became the first Australian to appear at four different World Cup finals (2006, 2010, 2014 and 2018).
- Peru scored as many goals in this match as they managed in their previous eight World Cup games combined.
- Australia have not kept a clean sheet in any of their 13 matches at their last four World Cups between 2006 and 2018.
- Australia's failure to win any of their three matches at the 2018 World Cup mean that Oceania countries (Australia and New Zealand) have now won just two of their 22 matches at the World Cup finals (drawn seven, lost 13).
'Proud of the fans' - what they said
Australia coach Bert van Marwijk: "It's a little bit of a different feeling after this game.
"I heard Denmark played a draw, so even if we won by three or four goals it wouldn't have mattered, other than the feelings for the players.
"I liked the period of time I worked with these guys. I learned from them and I learned from their mentality.
"The way they improved, you don't see that that often on this level. I hope they learned something in the past few months. They can learn from good things but also from bad moments."
Peru coach Ricardo Garceca: "It is a joyful feeling. This was a very difficult match in terms of psychology, we had to be strong after we had lost unexpectedly twice.
"We played against a team who is a tough, very strong and physical team and they could qualify so their players made a huge effort.
"In the stadium we had all of these people supporting us. We can leave the World Cup with our heads high."
Andre Carrillo, who scored Peru's first goal: "I am very grateful to all the Peruvian fans. Many people made the impossible trip to be here.
"I am happy to give them the victory. We are proud of them."
- 5MilliganBooked at 88mins
- 15JedinakBooked at 10mins
- 10KruseSubstituted forArzaniat 58'minutesBooked at 60mins
- 23RogicBooked at 66minsSubstituted forIrvineat 72'minutes
- 9JuricSubstituted forCahillat 53'minutes
- 13TapiaSubstituted forHurtadoat 63'minutesBooked at 79mins
- 19YotúnBooked at 45minsSubstituted forAquinoat 45'minutes
- 18CarrilloSubstituted forCartagenaat 79'minutes
- Sergei Karasev
- Shots on Target
Second Half ends, Australia 0, Peru 2.
Foul by Tim Cahill (Australia).
Luis Advíncula (Peru) wins a free kick in the defensive half.
Corner, Peru. Conceded by Aaron Mooy.
Foul by Mile Jedinak (Australia).
Edison Flores (Peru) wins a free kick in the attacking half.
Mark Milligan (Australia) is shown the yellow card for a bad foul.
Foul by Mark Milligan (Australia).
Christian Cueva (Peru) wins a free kick in the attacking half.
Corner, Australia. Conceded by Miguel Trauco.
Attempt missed. Mile Jedinak (Australia) right footed shot from outside the box is too high from a direct free kick.
Daniel Arzani (Australia) wins a free kick in the attacking half.
Foul by Wilder Cartagena (Peru).
Offside, Peru. Paolo Hurtado tries a through ball, but Paolo Guerrero is caught offside.
Paolo Hurtado (Peru) is shown the yellow card for a bad foul.
Aziz Behich (Australia) wins a free kick in the defensive half.
Foul by Paolo Hurtado (Peru).
Substitution, Peru. Wilder Cartagena replaces André Carrillo.
Foul by Mile Jedinak (Australia).