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The result ensures that with one round of group games still to play, Paraguay qualify from Group A along with Chile, Argentina and Uruguay.
Nestor Pitana, the Argentine who refereed the 2018 World Cup final, waved play on when the ball bounced off him outside Colombia's box and Brazil continued passing for Roberto Firmino to head in an equaliser.
Brazil had won their previous nine games coming into the match in Rio de Janeiro, all bar one of them without conceding a goal.
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.
Peru, who reached the final of the last Copa America but had won just two of their 12 games since, got off to a good start in Goiania.
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.
The result means Brazil are the first team in the tournament to win both their first games, and immediately go to the top of Group B.
Paraguay went behind to an early penalty but scored three times in the second half for a 3-1 win over Bolivia.
Marquinhos, Neymar and Gabriel Barbosa scored in the opener at Man Garrincha stadium in Brasilia on Sunday.
Hosts Brazil take on Venezuela in the opening match at the Mane Garrincha Stadium on June 13.
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