Chile centre-back Waldo Ponce was initially credited following a goal-mouth scramble in the 92nd minute, but the official Copa America website later marked the score as an own goal by Peru's Andre Carrillo.
The result left Chile with an unassailable seven points at the top of Group C. They will play Group B's second-place getters in the quarter-finals - either Brazil, Paraguay or Venezuela - in San Juan.
Having booked their places in the quarter-finals before kick-off, neither Chile nor Peru looked particularly interested in winning their clash in Mendoza.
Peru coach Sergio Markarian rested nine players from their previous match while Claudio Borghi made six changes to the Chile's starting line-up.
Roared on by around 30,000 fans in the Malvinas Argentinas stadium, Chile created the first real chance of the match in the 14th minute when Jean Beausejour fired in a low cross from the left which Esteban Paredes just failed to reach.
Peru almost scored from a similar move in the 38th minute. Right-back Giancarlo Carmona provided the cross and Josepmir Ballon, stealing in at the back post, stretched out a leg but failed to direct the ball goal-wards.
Tempers frayed in the second half and both sides ended the match with 10 men after Beausejour and Carmona were sent off after an hour for their part in a melee that drew in all 22 players.
The match appeared to be heading for a goalless and increasingly tetchy stalemate until the scrappy late strike sealed the win for Chile.
