Uruguay's draw means all three seeded sides at the tournament have failed to win their opening matches. Hosts Argentina were held 1-1 by Bolivia, while Brazil's opener against Venezuela ended 0-0.
All 12 teams in the competition have now played a game, with four of the six matches ending in draws. Colombia and Chile are the only sides to have won, both by a single goal.
"Parity is a distinctive trait of modern football," Uruguay coach Oscar Tabarez said after his side's match, summing up the cagey opening games of the tournament.
"Before this competition there were those talking about favourites as if the games had been won before they'd even been played. We don't believe in that."
Uruguay, with Diego Forlan and Luis Suarez in attack, had been expected to beat a Peru side who finished bottom of the South American qualifying group for the 2010 World Cup.
However, it was the Peruvians who took the lead in the 24th minute of the Group C clash against the run of play.
Midfielder Michael Guevara hoofed a speculative pass through the heart of the Uruguayan defence and the two centre-backs stood like statues, waiting for offside.
But the flag stayed down, leaving Peru's lone striker Paolo Guerrero to round the goalkeeper and stroke the ball home.
Uruguay kept plugging away and in first-half injury time their perseverance paid off.
Nicolas Lodeiro squeezed the ball through to Suarez and the Liverpool striker buried his shot in the bottom left-hand corner of the net with virtually the last kick of the half.
Hours later in the same stadium, Chile also fell behind against the run of play, with Mexico's Nestor Araujo looping a header over goalkeeper Claudio Bravo just before halftime.
But the Chileans equalised in the 67th minute through second half substitute Esteban Paredes, who stole in at the back post to thrash the ball into the net from close range following a scramble in the box.
Six minutes later Arturo Vidal grabbed Chile's winner with a towering header from a corner, which rocketed into the top corner of the Mexican net.
The victory sparked wild celebrations in the stadium from around 15,000 Chileans, who have made the short trip across the Andes in freezing conditions to follow their team.
Mexico have been forced to field a sub-strength team at the tournament after eight of their players were suspended for disciplinary reasons on their way to Argentina.
