Firmino set up Jesus for the opener before the Manchester City man returned the favour, turning provider as Firmino scored to secure victory.
It meant Jesus got the better of his club team-mate Sergio Aguero, who kept the Brazilian out of City’s team for much of last season.
Jesus was unmarked when he fired Brazil into the lead after 19 minutes when Liverpool striker Firmino whipped in a low cross for his team-mate to side-foot home from close range.
Argentina were unlucky as they chased an equaliser, with Sergio Aguero heading against the bar with a header in the first half and Lionel Messi hitting the post 11 minutes after the restart.
And hosts Brazil had to endure a nervy wait until the 71st minute before they increased their lead at the Estadio Governador Magalhaes Pinto.
With Argentina chasing the game, Jesus and Firmino combined again on the counter-attack after great work from the City striker gave Firmino the simplest of tap-ins.
Argentina had five players booked as they battled for supremacy against their old rivals, with only Dani Alves given a yellow for Brazil as the 36-year-old turned in a solid defensive performance to keep Messi and Angel DiMaria quiet.
Sunday’s final in Rio de Janeiro will see Brazil face either Chile or Peru, who play in the early hours of Thursday morning (UK time).