SOCHI: A stunning Andre Carrillo volley gave Peru their first World Cup goal in 36 years before captain Paolo Guerrero grabbed a second as the Andean nation condemned Australia to a 2-0 defeat in Sochi on Tuesday and an early exit from Russia.

Guerrero set up Carrillo's 18th-minute wonder goal from the edge of the box with a delightful cross, then scored from a deflection five minutes after the interval to send Peru's red-and-white army of fans into ecstasy at the Fisht Stadium.

Although already eliminated, the Peruvians head home on a high note, having grabbed their first World Cup win since their 4-1 defeat of Iran at the 1978 finals in Argentina.

Denied a place at the global showpiece for 36 years, the result left Peru third in Group C with three points, while the Socceroos head home with just one, but more than a few regrets.

France topped the group with seven points, with Denmark runners-up on five after the teams played out a 0-0 draw.

Australia had needed to beat Peru and for France to defeat Denmark so the result was largely academic for the Socceroos.

But Bert van Marwijk's side would have felt it was deja vu, as they surged forward in numbers but lacked the polish to conjure a score.

Captain Mile Jedinak blazed over the bar in the fifth minute while winger Mathew Leckie was denied in the goalmouth by a scrambling defence in the 36th.

Not even an early second half injection of talisman Tim Cahill could spark the Socceroos, their 38-year-old striker denied a goal in his World Cup swansong when he fired a volley straight into a Peru defender.

Australia have long yearned for a cutting edge up front but it was a defensive error that allowed Guerrero to swoop and set up Carrillo's winner.

Full back Josh Risdon failed to deal with a long ball, allowing Guerrero possession at the left of the area, and the captain wheeled a cross into the path of winger Carrillo who hammered the ball into the left corner of the net.

It was the Andean nation's first World Cup goal since Guillermo La Rosa scored in a 5-1 defeat by Poland at the 1982 finals in Spain.

Australia tried to rally through midfielder Tom Rogic who barged through a nest of defenders into the box in the 27th minute only to have his shot blocked.

Guerrero, whose tournament was in doubt due to a doping suspension, doubled the score in the 50th minute, a deflection off Jedinak dropping the ball in his path obligingly before his shot rebounded off Mark Milligan into the net.

From there, Peru rode their luck to the finish as the Socceroos peppered the goal in desperation but to no avail.