The defending champion battled into the last four after beating Chile 1-0 despite playing almost all of the second half with 10 men following Gabriel Jesus' red card for an awful high challenge.
It has now gone 12 games in all competitions without defeat, keeping a clean sheet in nine of those, while Tite is yet to lose a match in this competition while in charge of the Selecao.
Should it reach the final this time around, the 60-year-old will equal Mario Zagallo as the Brazil coach with the longest unbeaten run in Copa America history (12 games).
Standing in the host's way is a Peru side which came through a thrilling quarter-final against Paraguay, which ended 3-3 after extra time and with each side down to 10 men.
In the end, Miguel Trauco's sudden-death penalty secured Peru's place in the semi-finals for the fourth time in five tournaments.
Head coach Ricardo Gareca has only managed to beat Brazil twice in 10 attempts, with their previous meeting in the 2021 group stage ending in a 4-0 win for the five-time world champions.
Brazil has also not lost a Copa America match on home soil since 1975 – but that 3-1 defeat came at the hands of Peru in the semi-final first leg of their triumphant campaign.
PLAYERS TO WATCH
Brazil – Lucas Paqueta
Lyon midfielder Lucas Paqueta needed less than a minute on the pitch as a half-time substitute before scoring what proved to be the winner against Chile.
With Jesus suspended and Roberto Firmino not wholly convincing at these finals, Paqueta may well have a key role to play here.
Peru – Yoshimar Yotun
With a goal, an assist and a converted spot-kick in the shoot-out, few Peru players did as much to drag them into the final four as Yoshimar Yotun.
The Cruz Azul midfielder is a versatile asset at the heart of the side and could be equally important in disrupting Brazil's rhythm and getting Peru up the pitch when possible.
- Brazil will host Peru for 20th time in competitive games (W15 D2 L2). One of those defeats was in the 1975 Copa America, the last time Brazil lost a game at home in the competition (3-1).
- Tite has never lost a game in the Copa America (W8 D3). If Brazil reach the final, Tite will equal Mario Zagallo as the Selecao boss with the longest unbeaten run in the competition's history (P12 W10 D2).
- Ricardo Gareca will face Brazil for the 10th time (W2 L7), and the sixth in this competition (W1 L4). Peru is unbeaten in its past 12 Copa America games when Brazil was not its opponent (W6 D6).
- Brazil is the top-scoring team in this year's finals (11), eight of their goals coming in the second half and five in the last 15 minutes, each more than any other team in the competition.
- Peru is the team with the fewest shots on target among the semi-finalists (18), but it is second for shot conversion rate (16.3 per cent).