Tite’s men beat their final opponents 5-0 during the group stage but were under pressure when Peru skipper Paolo Guerrero cancelled outEverton‘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 forEvertonto 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.
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.