Jesus opened the scoring after 19 minutes when he side footed in a low cross from Firmino.
Sergio Aguero and Lionel Messi both struck the woodwork for Argentina, who have not beaten Brazil in a major competitive fixture since 2005.
A Firmino tap-in secured the win to set up a final against Peru or Chile.
Brazil’s win came at the same Mineirao stadium in Belo Horizonte where they were thumped 7-1 by Germany in the 2014 World Cup semi-finals.
Argentina forward Lionel Messi, who has won 29 trophies with Barcelona, has yet to win a major title with Argentina with his only success being a 2008 Olympics gold medal.
His next chance to change that will be when Argentina co-host the 2020 Copa America, with Colombia.
“Something new is on the horizon,” said the 32-year-old, who quit international football after his country’s defeat by Chile in the 2016 Copa America before returning for the 2018 World Cup.
“I hope we are respected and not criticised. They should let the team be and let them grow.
“The truth is I have got on very well with this group of players and if I have to help in some way I will. This is a great group which is growing and if I can join them I will.”