Tite's side grew in confidence and began to dictate the tempo, but on the stroke of half-time, the referee awarded Peru a disputed penalty when Thiago Silva inadvertently handled in the box. Paolo Guerrero slotted home with his third goal of the tournament, joining Everton as the competition's top goalscorer.
The hosts responded in style to conceding their first goal of the tournament, however, with Jesus restoring Brazil's lead with a smart finish after being played through by Firmino in stoppage time.
After the restart, Philippe Coutinho curled a lovely shot agonisingly wide, while Firmino spurned a half-decent opportunity, screwing wide from inside the box as Brazil piled on the pressure.
They were soon reduced to 10 men, however, as Jesus was given his marching orders for a second bookable offence - a decision that looked incredibly harsh and left the Manchester City forward in floods of tears.
In the end it mattered little as Brazil secured their ninth Copa America title in style as Richarlison made it 3-1 from the penalty spot after Everton was clattered by Carlos Zambrano.
The supporters in Rio de Janeiro will party into the night after a fine tournament in which their team scored 13 times and conceded only once, knocking out fierce rivals Argentina along the way.
TALKING POINT - Tite delivers long awaited silverware
After some troubled years, Brazil have finally landed some much-needed silverware. Five years on from their traumatic World Cup exit at the hands of Germany on their home soil, they finally claim their first trophy for the first time in 2007. Credit must go to Tite, who has overcome multiple set-backs, including last year's World Cup defeat to Belgium, and delivers the 2019 Copa America title even without star man Neymar. Surely now the rumours about his future as Brazil's long-term coach will disappear.
MAN OF THE MATCH - Everton (Brazil)
In the absence of Neymar, Brazil needed a hero and boy did the talent from Gremio step up to the plate. Gabriel Jesus was sensational - until he was sent off - but Everton's rise to fame continued with yet another star performance. He terrorised the opposition defence with his explosive pace, trickery and his general brilliantness, while his intelligent movement off the ball and clinical finishing yielded the breakthrough. A wonderful Copa America performance has put the 20-year-old on the map and the clamour for his signature begins amongst Europe's elite.
15' - GOAL! Brazil 1-0 Peru: Jesus collects on the right flank, skips past a challenge and delivers a deep cross for Everton who sneaks in at the far post and, with their first shot on goal, Brazil lead!
43' - PENALTY TO PERU! Very harsh on Brazil. Cueva's cross is blocked by the hand of Silva, completely accidentally, but the referee points to the spot. But wait... it's going to VAR! What's the referee going to do here? THE PENALTY STANDS! Peru with a golden opportunity to equalise...
44' - GOAL! Brazil 1-1 Peru: Guerrero keeps his cool, sending Alisson the wrong way as he tucks the ball in the bottom corner. Game on!
45'+ 2 - GOAL! Brazil 2-1 Peru: Jesus restores Brazil's lead with a well-taken goal. The City forward drops off the shoulder of his marker to latch onto Firmino's through-ball and he sticks the ball past Gallese in the Peru goal. What a time to strike!
70' - JESUS IS SENT OFF! Wow. A second bookable offence and the best player on the pitch tonight is given his marching orders. It's incredibly harsh. The Man City forward had his eyes firmly focused on the ball while challenging for a high ball, but receives the yellow card for barging into his opponent.
87' - PENALTY TO BRAZIL! Everton's mazy run is ended by the shoulder of Zambrano. The defender clatters into the youngster inside the box quite needlessly as he had just overrun the ball. The referee points to the spot, checks with VAR and then decides the penalty must stand.
90' - GOAL! Brazil 3-1 Peru: Richarlison drills the ball into the bottom corner, ripping off his shirt and sending the supporters wild! Brazil are now the 2019 Copa America winners, surely! Job done.
Tite is the first manager to win the Copa America (Brazil - 2019), Copa Libertadores (Corinthians - 2012) and Copa Sudamericana (Internacional - 2008).
Brazil's Gabriel Jesus is the first player ever to score a goal and be sent off in a Copa America final.
Alisson conceded a goal after 889 minutes with a clean sheet in all competitions; he had last conceded on May 4th in the Premier League game between Liverpool and Newcastle United (Salomón Rondón, 54').
Everton scored with Brazil's first shot attempted against Peru - the previous time a team had scored with their first shot in a Copa America final had also been Brazil, in 2007, against Argentina (Julio Baptista, 4').
Everton's goal for Brazil was the first goal in a Copa America final since 2011 (Diego Forlan, 90th minute, Uruguay 3-0 Paraguay), after 255 goalless minutes in the final game.