The 35-year-old forward reached the landmark when he opened the scoring on 20 minutes in Santiago del Estero.
Chelsea midfielder Enzo Fernandez also scored, before Argentina paraded the World Cup trophy in front of more than 42,000 supporters.
It was Argentina’s second match on home soil since beating France in Qatar on penalties in December to win the World Cup.
Messi scored his 800th career goal – and 99th for Argentina – in a 2-0 win over Panama in Buenos Aires last week as part of the team’s World Cup homecoming tour.
The Paris St-Germain striker reached three figures for his country when he took a pass from Villarreal’s on-loan Tottenham Hotspur midfielder Giovani lo Celso and fired a low shot into the bottom corner.
Three minutes later Nicolas Gonzalez outjumped goalkeeper Eloy Room to head home from four yards before the Fiorentina winger set up Messi for his second of the night.
Fernandez made it 4-0 with a shot from distance before Lo Celso released Messi to notch his third in just the 37th minute.
Angel di Maria and Gonzalo Montiel rounded off the scoring in the second half but the night belonged to Messi, who extended his record as Argentina’s all-time record scorer – Gabriel Batistuta is a distant second on 56.
He remains third on the men’s all-time international scoring list behind Portugal’s Cristiano Ronaldo (122) and Iran’s Ali Daei (109).