It ended with Lionel Messi being sent off and boycotting the medal ceremony to protest the refereeing.
"We shouldn't take part in this corruption," an unusually outspoken Messi said. "There was lack of respect toward us during this Copa América. We could have done better, but they didn't let us make it to the final. Corruption and the referees are not letting the fans enjoy football. This is ruining football."
Messi had already complained about the refereeing after Argentina's loss to Brazil in the semifinals, hinting the result was expected because the hosts were allegedly in charge of South American soccer. He said he expected Brazil to win Sunday's final against Peru, claiming it was already set up for the hosts' victory.
When asked if he didn't fear being suspended for his comments, Messi said "the truth needed to be told."
CONMEBOL, South America's soccer confederation, later released a statement condemning the "unacceptable" and "baseless accusations" that discredited the Copa América's integrity.
"In football, sometimes you lose and sometimes you win," the statement said. "One of the fundamental pillars of fair play is to accept the results and the refereeing decisions with respect."
Messi was sent off after getting involved in an altercation in a tense third-place game between the rivals from the last two finals of the South American competition.
Veteran Chile midfielder Gary Medel also was red carded after the first-half shoving match with Messi at the Arena Corinthians.
Sergio Agüero and Paulo Dybala scored early for Argentina, and Arturo Vidal put Chile on the board with a second-half penalty kick.
Chile had beaten Argentina in the final in 2015 and 2016, both times in penalty shootouts.
It was a heated match from the start in São Paulo, with many hard fouls from both sides and altercations involving several players.
None was bigger than the one sparked by the Messi-Medel confrontation that led to the red card for both players in the 37th minute.
It started when Medel wasn't happy that Messi came in from behind to try to gain possession. The Chilean turned around to confront the Argentine star, who didn't back down. They started to bump into each other with their chests and shoulders and Paraguayan referee Mario Diaz de Vivar came in to immediately send both players off.
"A yellow card should have been enough for both players," Messi said.
Messi had also received a straight red card in his national team debut with Argentina in a friendly against Hungary in 2005.
Argentina opened the scoring after Messi quickly took a free kick with a long through ball to Agüero, who went past goalkeeper Gabriel Arias before finding the net in the 12th minute. There was some complaint that the ball was rolling when Messi took the free kick that caught the Chilean defense by surprise.
Dybala added to the lead with a shot from inside the area in the 22nd, and Vidal gave Chile hope of a recovery by converting a penalty awarded by video review in the 59th.
Argentina is enduring a 26-year title drought with the senior team. Messi's only title with Argentina was with the under-23 squad at the 2008 Beijing Olympics.