The Barcelona midfielder was shown a straight red card towards the end of the first half following a confrontation with former Cardiff midfielder Gary Medel, who was also dismissed.
Messi, though, appeared to have been hard done by, with Chile defender Medel appearing to push his head towards the Argentina playmaker as they squared up, chest to chest.
Argentina, beaten by hosts Brazil in the semi-final, had taken an early lead through Manchester City forward Sergio Aguero.
Chile – whose semi-final defeat by Peru ended hopes of a third straight Copa America title – saw Manchester United forward Alexis Sanchez forced off with a suspected hamstring problem before Paulo Dybala made it 2-0 after 22 minutes
After Messi and Medel were dismissed by Paraguay referee Mario De Vivar, who had consulted a video replay of the incident, Arturo Vidal’s penalty pulled a goal back from Chile on the hour, with the VAR again called into action.
Aguero squandered a couple of late chances to put the result beyond doubt, but Argentina saw out the closing stages to secure third place as their trophy drought goes on.
Messi had made an early impact when his quick ball forwards from a free-kick just inside his own half put Aguero racing clear and the Manchester City striker went around the goalkeeper and opened the scoring in the 13th minute.
Chile were then forced into a change when Sanchez limped off and Junior Fernandes came on.
Argentina doubled their lead in the 22nd minute. Juventus forward Dybala was played into the left side of the Chile penalty area and clipped an angled shot into the far corner.
Dybala sent another volley just wide before tempers boiled over as half-time approached when Medel and Messi squared up after chasing a ball going out on the touchline.
Argentina remained a threat on the counter at the start of the second half, but Chile were given a way back into the match.
Play was called back as the referee looked at a potential foul by Argentina’s Giovani Lo Celso on Charles Aranguiz on the edge of the penalty area and eventually pointed to the spot.
Despite the delay, Barcelona midfielder Vidal remained calm, drilling the penalty straight down the middle as Argentina goalkeeper Franco Armani dived away.
Fernandes and fellow substitute Diego Vargas both tested Armani before Argentina slowly regained control, with Aguero having a couple of late chances to score again.
In stoppage time, the Chile bench were all up claiming for handball, but this time there was no extensive VAR review as the appeals were swiftly waved away.
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Speculation in local media following the semi-final victory over arch-rivals Argentina in the week suggested the 58-year-old would not be continuing in his role after the end of the tournament.
That led to the unusual step of the Brazil football Confederation publicly confirming the coach would stay on.
“The Brazilian football Confederation expresses its confidence in the work of the coaching staff of the Brazilian national team and reaffirms that it will be maintained on a permanent basis,” said a statement.
Casemiro added his full support for the manager.
“He has won a lot of national and international titles, and he is a victor,” he told Brazilian journalists.
“He’s a coach who has been in the position for three years and has (won) more than 80 per cent.
“Tite is in our heads to be mentally strong, not to destabilise (us).
“He has a great success in this, to make the team concentrate and not to fall in the trap of the opponents, to let them provoke us, so people do not fall for it.”
Speaking ahead of the game, Tite said the side would prepare for every eventuality.
In quotes on Spanish outlet AS, he said: “We have to prepare ourselves for all the circumstances of the game. If we score a goal, we have to continue to play well.”
Brazil saw off Peru 5-0 in the group stage, but Tite said: “The teams come with different strengths and we know the difficulties we will have with Peru, (5-0) did not reflect what happened on the pitch.”
Brazil are favourites to win Sunday’s final, at the Maracana, but Peru’s Argentinian coach Ricardo Gareca has confidence in his side.
“When you make it to the final, you have to try to win it. There’s no other option,” he said.
“We reached the final thanks to our own merits. This group is very strong. I think that’s the key. It has the strength to overcome adversities.
“We have the players to do it. We are peaking right now. If I had to choose a time to make it to the final, it would be now.
“But we know that it will be difficult against Brazil no matter how we are playing.”
Veteran striker Paolo Guerrero, whose goal in Wednesday’s win made him the highest Copa America scorer (13) among players still currently active, is not worried about the fact few are giving his side a chance.
“You can call them favourites if you want to. But for us, there are no favourites on the field.
“We have to stay humble and do our job. There are a lot of people not showing respect for Peru right now. I have a lot of respect for Brazil, but I also respect my country.”
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Tite’s men are huge favourites to take the title after disposing of arch rivals Argentina 2-0 in the semi-finals, especially as they have already beaten Peru 5-0 during the group stage.
But Peru are buoyant after recovering from that horrendous result to march to their first final since 1975, and the hosts can expect a much stiffer examination this time around.
Let’s take a look at the big pre-game talking points.
PREMIER LEAGUE STARS TO SHINE AGAIN?
Brazil haven’t always been able to produce free-flowing football during the course of this tournament, with their troubles in getting past Argentina – who dominated large chunks of Tuesday’s semi-final and twice hit the woodwork – underlining the sensation that this is far from a vintage Brazilian side.
However, they were able to conjure a pair of outstanding goals to progress to the final, with the team’s Premier League-based forward line of Roberto Firmino and Gabriel Jesus making the difference.
The opener against against Argentina was set up by Firmino with a precise cross to give Jesus a tap-in, before the tables were turned for the second goal as the Manchester City man embarked upon a scintillating counter-attack to give the Liverpool forward a simple finish.
The understanding between Firmino and Jesus is the biggest threat to a Peruvian backline which has gone way beyond expectations to keep clean sheets against both Uruguay and Chile in the knockout rounds, and will now be aiming to prove the group stage humiliation against this weekend’s opposition was just a very bad day at the office.
The hosts could also do with Philippe Coutinho stepping up after a mediocre tournament, while flying winger Everton’s place is under threat following a pair of sub-par performances. But on current form, the Premier League duo could be the men who matter.
ANOTHER CLEAN SHEET FOR BRAZIL?
Ever since Pele and co wowed the world in 1958, Brazilian football has always been synonymous with creative and exciting attacking play – nobody does the beautiful game better, according to the popular stereotype.
In the last couple of decades, however, a succession of national teams have followed a far more pragmatic approach, with just as much emphasis on defence as attack.
And that is certainly true of the current crop, with Tite’s team basing their challenge on a highly organised defensive unit which has not conceded a single goal so far.
The central defensive partnership of Thiago Silva and Marquinhos, backed up by Liverpool keeper Alisson and Real Madrid’s midfield destroyer Casemiro have formed a formidable spine, keeping clean sheets in seven consecutive games including pre-tournament friendlies.
So it might not be traditionally Brazilian, but don’t be surprised if the hosts lift the trophy by grinding out a 1-0 victory – because this particular team is defined far more by rigid defensive organisation than by joyous attacking flair, and they will be more inclined to protect a narrow lead than take any risks by chasing a bigger margin.
PERU ON THE ATTACK?
The most compelling tactical question ahead of the contest is how Peru will approach the game, because their tactics have differed markedly in the two previous knockout ties.
In the quarter-final against Uruguay, Ricardo Gareca’s men were happy to defend their penalty area, limiting their attacking ambitions and forcing their opponents to play their way through. The ploy worked, with a goalless draw after 90 minutes being followed by a ruthless display of penalty-taking in a shoot-out triumph.
The semi-final against Chile, however, was a very different matter as Peru got onto the front foot from the opening whistle, exploiting the wily movement of veteran forward Paolo Guerrero, the penetration of skilful wingers Andre Carrillo and Edison Flores, and the creative passing of playmaker Christian Cueva.
Whether Gareca dares to employ such a bold strategy in the daunting surroundings of a final against Brazil in the Maracana remains to be seen, but the vitality and dynamism of Peru’s semi-final performance suggests they are determined not to go down on the back foot, and the hosts cannot simply assume they will spend the whole game attempting to pick their way through massed ranks of red and white shirts camped inside their own penalty area.