Lucas Paqueta gave Brazil an lead early in the second half before Jesus was sent-off within two minutes for a high kick on Eugenio Mena.
Chile piled on pressure but the closest they came to an equaliser was Ben Brereton’s header hitting the bar.
Peru advanced after beating Paraguay 4-3 on penalties after a 3-3 draw.
“Jesus was just bad luck,” said Brazil forward Neymar after the win against Chile. “He had his eye on the ball, not on the man, and unfortunately, he was sent off.
“Every day that goes by we have tests to make us stronger, to prove that we can play under all kinds of circumstances.
“Chile are a good team, they have great players and it is very difficult with a man less. Everyone deserves praise – the defence, the midfield, the forwards.
“We managed to withstand something that rarely happens to this team. It was a big test for us.”
Peru came through an action-packed game against Paraguay, who took the lead through captain Gustavo Gomez early on.
However two goals from Gianluca Lapadula put Peru in front and, despite Paraguay having Gomez dismissed just before half-time, they equalised through Junior Alonso.
Yoshimar Yotun restored Peru’s lead but, after they went down to 10 men when Andre Carillo was sent off in the 84th minute, Gabriel Avalos scored a last-minute leveller to send the tie to penalties.
Paraguay missed with three of their spot-kicks before Miguel Trauco scored the decisive penalty for Peru.