Neymar beat three defenders on the left before crossing for Paqueta to guide home the semi-final’s only goal.
Brazil, who have won the Copa America every time they hosted the tournament, face either Argentina or Colombia in Saturday’s final at the Maracana.
“I want Argentina, I am cheering them on,” Neymar said.
“I have friends there and in the final Brazil will win.”
Paris St-Germain forward Neymar was a bright spark for Brazil as they again edged Peru, the side their beat in the 2019 final to lift the trophy for the ninth time.
Peru goalkeeper Pedro Gallese made a fine double save from point-blank range to deny Neymar and Richarlison early on.
Neymar’s trickery and ability to find Paqueta with a finely placed pass when surrounded by Peruvian defenders on the left proved decisive in the 34th minute.
Peru pressed for a second-half equaliser, with Gianluca Lapadula testing Ederson with a fierce effort, but they failed to upstage the hosts.