Paquetá's winner to the left corner of Chilean goalkeeper Claudio Bravo in the 46th minute gave Brazil fans some hope that the Selecao would ease into the next stage.
Argentina topped its group with three wins and one draw, and Messi in great shape. The captain scored three goals in the four games while setting a record for most Argentina caps.
Regular time at the Olimpico Stadium in Goiania finished 3-3 after a hard-fought match that included red cards to key players of both teams and two goals by Italian-born Gianluca Lapadula for Peru.
Defending champion Brazil and Chile will have their star players back in action when they meet in the Copa America quarterfinals on Friday.
Messi has some of the best statistics so far at the Copa America and hee capped the group stage on Monday with two goals and an assist in Argentina's 4-1 win over Bolivia.
The hottest competition could be on the other side of the draw, where arch rivals Argentina and Uruguay have the chance to meet in the semifinals.
Edinson Cavani scored his 2nd goal at the Copa America and it turned crucial as the 1-0 win over Paraguay allowed his nation an early meet with Brazil in the knockout stages.
The Barcelona superstar also became Argentina's most capped international player on Monday as this was his 148th appearance for Argentina.
Messi's two goals and one assist helped Argentina ensure top spot in Group A, setting up a quarterfinal against Ecuador on Saturday.
Edinson Cavani scored from the penalty spot in the 21st minute for the only goal of the match at the Nilton Santos Stadium in Rio de Janeiro.
Brazil's quarterfinal on Friday against Uruguay or Chile will be in Rio de Janeiro at Nilton Santos Stadium, of which the field has been heavily criticized since the start of the tournament.
Uruguay vs Paraguay Copa America 2021 Live Streaming: Find full details on when and where to watch URU vs PAR online.
Record-chasing Lionel Messi doesn't want to rest at the Copa America despite Argentina already having secured its place in the quarterfinals.
Bolivia vs Argentina Copa America 2021 Live Streaming: Find full details on when and where to watch BOL vs ARG online.
Neymar, defender Thiago Silva and striker Gabriel Jesus didn't play against Ecuador at the Olimpico Stadium in Goiania.
Brazil vs Ecuador Copa America 2021 Live Streaming: Find full details on when and where to watch BRA vs ECU online on SonyLIV.
Weeks ago, after Brazil became last-minute hosts of Copa America, organizers scheduled seven matches for the Nilton Santos stadium in Rio precisely because the pitch at the Maracana was worn out.
Tite said in a news conference on June 12 that the Copa America was shifted to his country in a “confusing manner."
Uruguay will end its group stage campaign on Monday against Paraguay in a match that could decide which team faces defending champions and favorites Brazil in the quarterfinals.
Referee Pitana accidentally blocked a pass by Neymar about 10 meters in front of the Colombian area in the 78th minute which eventually led to a goal.
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