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Brazil were on top in the first half but it took them 35 minutes to break the deadlock thanks to a side-footed volley from Paqueta after nice work by Neymar.
Brazil were unbeaten in 11 games and topped Group B, while Chile finished only fourth in Group A.
Peru take on Paraguay in the first quarterfinal.
The result means that Argentina will face Ecuador in the last eight on Saturday while Uruguay, who beat Paraguay 1-0, will play Colombia the same day.
The draw at an empty stadium in central Brazil marked the first time Brazil have not picked up a win since they lost 1-0 to Argentina in a friendly in November 2019.
The result ensures that with one round of group games still to play, Paraguay qualify from Group A along with Chile, Argentina and Uruguay.
The victory in Brasilia was Argentina's second 1-0 win in a row in this tournament and their 16th match without defeat since losing in the Copa America semi-final in 2019.
The IATA travel pass is a mobile app that can be used by passengers to obtain and store their COVID-19 test results from accredited laboratories.
Thousands of Brazilians protested against President Jair Bolsonaro's management of the pandemic in nationwide demonstrations on Saturday, blaming the administration for the high death toll and calling for the president's ouster.
The result in a game that was end-to-end but lacking in real excitement at a cavernously empty stadium in Brasilia leaves Uruguay joint bottom of Group A with no points.