The game, which was higher on tension than quality, witnessed 10 cards in total and two red cards -- one apiece -- early on, causing extreme fatigue on both sides and noticeably slowing the match’s tempo down the stretch.
Marcelo Diaz was shown a red on double a booking in the 28th minute after colliding with Messi. Fourteen minutes later, Arturo Vidal went to the pitch after a heavy challenge from Marcos Rojo, who was sent off directly.
The teams produced few chances in regular time, with Chile registering its first shot on target in the 79th minute.
When the final whistle was blown after 90 minutes of regular time, players on both teams collapsed in exhaustion, before gearing up for another 30 minutes of extra time.
Despite fatigue setting in, neither team appeared willing to settle for penalties as they fought hard in midfield clashes and sought counter attacks.
In the 9th minute of extra time, Chile's Eduardo Vargas came close to breaking the deadlock with a diving header, which was caught by Sergio Romero.
In the 24th minute, Messi won a free kick 22 meters from the goal, but Chilean goalkeeper Cladio Bravo managed to parry it to corner, and the extras too ended dry.
In the penalty shootout, both teams missed their first attempts. Chile’s Vidal failed to impress with a weak shot to the goalkeeper’s left, which Romero cleaned up with ease. Next, Messi missed even worse, failing to hit the target.
The loss is Argentina's third in a row in a major tournament after failing to triumph against Germany in the World Cup in 2014 and losing to Chile last year in the Copa America.
La Albiceleste has failed to win a Copa since 1993.
Some Argentina fans were seeing shedding tears at MetLife Stadium in New Jersey, along with their captain.
Argentina’s national team is worth three times that of Chile -- according to Transfermarkt.com, a football transfer stats website -- with 527 million euros against 169 million euros.
On the way into the finals, Messi-led La Albiceleste beat Venezuela 4-1 in the quarterfinals before decimating the U.S. hosts 4-0 in the semifinals in dominating fashion.
For its part, Chile destroyed Mexico 7-0 in the quarterfinals stage and beat Colombia 2-0 in a match that was interrupted by a two-hour rain delay.
The 2016 Copa America Centenario, held in 10 cities across the United States was a special edition of the tournament celebrating its hundredth anniversary, and the first iteration held outside South America.