The 35-year-old Messi bagged his landmark 100th goal after 20 minutes in Santiago del Estero before adding his 101st and 102nd in quick succession later in the first half.
Nicolás González and Enzo Fernández also scored to give Argentina a 5-0 lead at halftime against Curaçao, ranked 84 places below the world champion in the FIFA rankings.
The match remained goalless for much of the second half, but Ángel Di María converted from the penalty spot and Gonzalo Montiel scored after Paulo Dybala’s cross in the final 15 minutes to complete Argentina’s rout.
Messi’s latest milestone comes days after he scored his 800th career goal in a friendly against Panama on Thursday.
He is currently third overall in the list of top international goalscorers, 15 behind Portugal’s Cristiano Ronaldo and seven behind Iran’s Ali Daei.
“I hope there will be more [goals from Messi], he deserves all the praise, and it’s good that these goals have been on Argentine soil, that has a special value too,” Argentina coach Lionel Scaloni told reporters, according to Reuters.
Tuesday’s game was also a continuation of Argentina’s World Cup celebrations as players wore commemorative jerseys during the presentation of a replica trophy in front of thousands of fans.