Messi, who was moved to tears after the game as the Copa America was presented to the fans at the Monumental, took his international goals tally to 79.
The Paris Saint-Germain attacker opened the scoring after a nutmeg in the 14th minute, before doubling La Albiceleste’s lead in the 64th minute.
Messi rounded out the win and completed his hat-trick with an 88th minute strike.
The 34-year-old overtook Pele’s mark off 77 goals and usurped it with two more strikes.
Argentina boss Lionel Scaloni praised Messi, when he said: “I am proud to have him as a player. Messi is leaving a legacy to all the football players of the national team.
“Messi was always a player who made a difference, before and now. Winning (the Copa America) magnified everything, and if before he was already an idol of the people, now it’s much more.
“Seeing them excited fills us with joy, but it lasts only until this is over, because afterwards we have to continue working.”
The result maintains Argentina’s unbeaten run in 2022 World Cup qualifying, while Brazil remained perfect with a 2-0 win over Peru.
Neymar scored one goal and set up the other for Everton Ribeiro in the win in Recife.
Uruguay scored late to win 1-0 over Ecuador to stay third, while Paraguay edged Venezuela 2-1 and Colombia won 3-1 over Chile who are eighth.