The Barcelona star has now turned out 148 times for his country, moving him ahead of former Barca teammate Javier Mascherano, who had 147 caps. Messi scored twice in the win, with Papu Gomez and Lautaro Martinez also on target as Argentina reached the quarter-finals of the tournament as group winners.
Ex-Inter Milan defender Javier Zanetti held the record before Mascherano and completes the podium with 143 international appearances.
With 75 goals for Argentina, Messi is also his country's all-time leading scorer, having moved past Gabriel Batistuta (54 goals) in 2016.
Sergio Aguero, who won his 100th international cap against Bolivia, is third in the rankings with 42 goals.
Messi, who turned 34 last week, has won everything in the game at club level but is yet to taste success in senior international football.
He won the Under-20 World Cup in 2005 and an Olympic gold medal with Argentina's U23s in 2008, but has lost four major finals with the first team.
With Messi in the side, Argentina were beaten by Germany in the 2014 World Cup final and have lost at the last stage in the Copa America in 2007, 2015 and 2016.
As Messi focuses on winning a first major trophy with his country this summer, his future at Barca remains unresolved.
His contract with the club expires on Wednesday and if a new deal is not agreed upon before then, he officially becomes a free agent on Thursday.
However, Barca are working hard to reach an agreement over a new contract and are confident he will extend his 20-year relationship with the club.