The Argentina captain has now scored 57 free kicks in his career, one more than Portugal captain Ronaldo. Messi is five goals short of Diego Maradona's career tally of 62 free kicks.
Not to be outdone, Ronaldo made history of his own when he netted twice in Portugal's 3-0 win over Hungary on Tuesday, making him the leading scorer in the European Championship history with 11 goals in a men's record fifth tournament appearance. However, the goals came via a penalty kick and a tap-in during injury time.
Messi also became Argentina's all-time leading goalscorer in official games with his strike, bagging his 39th goal in 98 games for the Albiceleste and surpassed Gabriel Batistuta, who scored 38 before retiring after the 2002 World Cup.
Messi's strike was his 10th goal at the Copa America while he has netted six in World Cups and 23 in qualifiers. The Barcelona forward has scored a total of 73 goals for Argentina.
Messi, 33, also joined Americo Tesoriere (1920-25) as the only players to have featured in six Copa Americas for Argentina.
Chile goalkeeper and former Barca teammate Claudio Bravo praised Messi after the match and said: "Messi has a strike that few have in the world. He has a different precision from the rest.
"I had to suffer today. Football is like that. One enjoys himself when you face the best players, when they test you."
Messi did not dwell on his achievements, and when asked how he felt being the best player on the pitch in Monday's draw, he said: "We wanted to start with a win. It was important to start with a win against a difficult rival.
"Now we have Uruguay, another complicated game. That is why we needed to have started with a victory."