In a repeat of the 2019 Copa decider, Lucas Paqueta settled the semi-final contest with his 35th-minute goal in Rio de Janeiro.
Brazil will face either Argentina or Colombia in the decider after Tite made history by equalling Mario Zagallo as the Selecao head coach with the longest unbeaten run in Copa America history (12).
Tite's Brazil started on the front foot as Peru goalkeeper Pedro Gallese was kept busy at Estadio Nilton Santos.
The first big chance of the game fell to Brazil in the eighth minute as Paqueta slid a wonderful pass to Richarlison, who rounded Gallese and cut the ball to Neymar but the latter was unable to direct his shot on target.
Gallese survived a nervy moment five minutes later after spilling Casemiro's long-range free-kick before managing to save it at the second attempt.
The heroics of Gallese continued to keep Brazil at bay, with the Peru shot-stopper somehow denying Neymar from close range as he then got up quickly to stop Richarlison's follow-up effort.
As Brazil found more and more space, the Selecao finally beat Gallese and broke Peru's stubborn resistance 10 minutes prior to half-time.
Richarlison released Neymar and he wriggled away from three players before looking up and cutting the ball to Paqueta, who made no mistake.
Brazil goalkeeper Ederson had been a bystander until he was called into action for the first time four minutes into the second half, keeping out Gianluca Lapadula after the Peru forward cut inside and fired a shot across goal.
Unlike the first half, Brazil were made to work by Peru and La Blanquirroja again tested Ederson just past the hour mark as Raziel Garcia tried his luck from distance with a tricky attempt.
There were shouts for a Brazil penalty with 19 minutes remaining when Richarlison went down under a challenge following a superb pass from Neymar, but the protests were waved away by the referee.
Peru had a great chance to level the match nine minutes from the end after Ederson completely missed his attempt to punch a free-kick away, but Alexander Callens' header sailed wide of the post.