Both teams won one, drew one, and lost one in the group stages, but Peru looked more convincing than their Andean neighbours in a tougher group, beating the promising Venezuela and holding World Cup quarter-finalists Colombia to a draw.
Having been aided up to this point by a disciplined defence and a little luck, Peru are now favorites to make it through to the last four for the second consecutive Copa.
Their coach is Ricardo Gareca, one of six Argentine managers at the tournament.
Bolivia notched their first Copa win since 1997 when they beat Ecuador in the group stage, and a goalless draw against a second-tier Mexico side was enough to see them through.
But their morale will have taken a beating after hosts Chile trounced them 5-0 in the last group game.
The quarter final will be played in Temuco in southern Chile. The cold winter temperatures will be unlikely to faze either Andean team, but neither side will welcome a smog so thick that it led the government to declare an environmental emergency in the city on Wednesday.
The statistics go in favour of Peru -- 'La Verde' Bolivia have won only one out of the last eight Copa America clashes between the two teams -- although Gareca was quick to praise his opponents on the eve of the match.
"If there is a trend and Peru is favourite we have to accept that. But we know that it is not the reality. Teams make progress in the Copa America because they have something good which justifies it," he told reporters after a training session.
Peru will be relying on veteran forwards Jefferson Farfan, from Schalke 04, and Bayern Munich's Claudio Pizarro, who scored one of Peru's two goals from the group stage after Farfan was sidelined with an allergy.
Bolivia's coach Mauricio Soria will be counting on striker Marcelo Moreno Martins and midfielder Martin Smedberg, who both found the net against Ecuador.
The winner will face in the semis either Chile or Uruguay, who are playing their quarter-final in Santiago on Wednesday.
(Writing by Rosalba O'Brien; editing by Toby Davis)
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