Tite's men beat their final opponents 5-0 during the group stage but were under pressure when Peru skipper Paolo Guerrero cancelled out Everton's opener with a 44th-minute penalty.
Jesus, whose excellent wing play laid on Brazil's first goal, restored the advantage in first-half injury time.
That set the five-time world champions' on course for their first major honour in 12 years, although a clumsy aerial challenge on Carlos Zambrano was enough to earn Jesus a second yellow card and set up a fraught finale - until substitute Richarlison dispatched a final-minute penalty to spark buoyant celebrations.
Peru began confidently before Brazil hit the front in the 15th minute.
Jesus got the jump on Miguel Trauco with a clever run before jinking around the full-back and crossing for Everton to finish gleefully on the half-volley.
Everton turned provider shortly afterwards as Philippe Coutinho shot wide from 10 yards and Roberto Firmino headed narrowly over in the 36th minute.
They were misses the Selecao would regret when referee Roberto Tobar upheld a harsh handball call against a prone Thiago Silva on review and Guerrero levelled from the spot.
Peru's joy was short-lived, however, as Zambrano's ill-timed slip allowed the razor-sharp Jesus to steal in for a cool finish.
GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOLLLLLLLLL DO BRAAAAASIL!— CBF Futebol (@CBF_Futebol) July 7, 2019
GABRIEL JESUS COLOCA O BRASIL NA FRENTE!
2 x 1 | #JogaBola #CopaAmérica #BRAxPER pic.twitter.com/XGDcddOapR
Coutinho fizzed a curling effort fractionally wide six minutes into the second period as Brazil pushed to increase their lead.
Jesus was shown remonstrating in tears on steps inside the stadium tunnel after his fifth foul of the game strained Tobar's patience too far.
Edison Flores sent a rasping strike wide before the action became unhelpfully fractious as far as Ricardo Gareca's men were concerned.
Zambrano then erred once more, bundling Everton over, and Richarlison was on hand to land the final blow.
What does it mean? Brazil finally taste glory as Neymar looks on
Ever since his emergence as a wonderkid at Santos, this has been the era of Neymar for world football's most celebrated international team. However, this first Copa since 2007 comes on the back of failed 2014 and 2018 World Cup campaigns. The former humiliation on home soil has now been exorcised, albeit with the stricken Paris Saint-Germain star on the sidelines.
All three final goalscorers would probably have had reduced roles had Neymar been around and how he fits into such a well-drilled and efficient outfit under Tite from this point on will be intriguing.
Jesus red should not overshadow huge step forward
The Manchester City striker was indebted to his team-mates in the end, but they kind of owed him one. Having scored one and created another in the semi-final win over Argentina, Jesus repeated the trick and looked a player reborn in international colours. The 22-year-old's scoreless outing at Russia 2018 and an often-testing season at club level felt like distant memories.
Zambrano slips up at the wrong time
The last time Jesus saw the Peru defender on the turf it was, of course, bad news for the man in yellow. But Zambrano's woeful error at precisely the moment Brazilian nerves were jangling could scarcely have come at a worse time. The needless foul to concede the late penalty summed up his outing.
Key Opta facts
- Brazil have won the Copa America on each of the five occasions they have hosted the tournament (1919, 1922, 1949, 1989 and 2019).
- Tite is the first coach to win the Copa America (2019), the Copa Libertadores (with Corinthians in 2012) and the Copa Sudamericana (with Internacional in 2008)
- Gabriel Jesus is the first player to score a goal and be sent off in a Copa America final
- Peru's goal ended Alisson's streak without conceding at 889 minutes in all competitions. The previous time he was beaten was in action for Liverpool, Salomon Rondon the scorer for Newcastle United on May 4
- Everton's opener was the first goal scored in a Copa America final since 2011 (Diego Forlan, for Uruguay v Paraguay).
CONMEBOL's scattergun approach to scheduling their flagship competition means Brazil must defend their title in Argentina and Colombia next year.