Andre Carrillo netted Peru's first goal of the tournament 18 minutes into the match, volleying a low strike from captain Paolo Guerrero's cross into the far corner.
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34-year-old Guerrero then doubled Peru's lead just five minutes after the halftime break to score the first World Cup goal of his career.
Australia needed to win their final Group C game to have a chance of reaching the knockout stage, while Peru had been knocked out of the tournament before the match.
The 2018 FIFA World Cup kicked off on June 14 and will continue until July 15, with the matches being played in 11 cities across Russia.