The Manchester City striker was dismissed for two bookable offences either side of half-time, having earlier set up Everton's opener and then scored the second himself after Paolo Guerrero had levelled with a penalty at the Maracana Stadium in Rio de Janeiro.
His premature departure left Brazil to fight out a tense conclusion during which substitute Richarlison struck from the spot to claim the trophy for the fifth time on home soil.
Tite's men who took the lead with 16 minutes gone when Jesus created space for himself down the right before crossing for striker Everton to volley home.
Brazil assumed control as Peru's efforts to respond yielded little and Philippe Coutinho fired just wide after latching on to a Roberto Firmino cross.
Peru were back in it a minute before the break when, after defender Thiago Silva was adjudged to have handled inside the box as he slid into a challenge, Guerrero sent Alisson the wrong way from the spot.
However, Brazil restored their lead in stoppage time when Jesus swept home Firmino's cross to bring an end to an eventful first half.
Coutinho and Firmino both went close as the hosts attempted to kill the game off immediately after the restart.
But Jesus' evening took a turn for the worse with 20 minutes remaining when he was sent off for a second bookable offence following a challenge on Carlos Zambrano, having been booked before the break for a foul on Yoshimar Yotun.
Peru sensed an opportunity, but their hopes died when Richarlison converted from 12 yards with two minutes remaining after Everton had been felled by Zambrano.