The manager cut a visibly distressed figure during the match, particularly after striker Gabriel Jesus was shown a second yellow card and left the match.
But despite losing such an important player, the 10-man Selecao lifted the Copa America for the ninth time and their first under Tite.
Tite, who was criticised after Brazil were bundled out of the quarter-finals at the last World Cup, told a post-match press conference: "I became the Selecao coach today.
"I have no words to describe this happiness.
"We get so caught up in work that we're just going to be happy tomorrow when we get home and can watch the best moments."
Jesus had a similarly extreme night of highs and lows.
The Manchester City player set up Everton Soares' goal on 15 minutes before snagging Brazil's second goal in the 45th, just a minute after Peru's Paolo Guerrero equalised with a penalty.
But in the 70th he received a second yellow card and was visibly upset as he left the pitch, punching the VAR booth and kicking a water bottle.
Moments later he was picked up on cameras as he sat weeping on the steps inside the tunnel.
Quoted on the Brazil website, the 22-year-old later said: "I'm happy to be part of this group. We won this championship... now it's time to celebrate."
Fellow forward Richarlison would not let illness stop him, with the Everton player taking to the field in the second half and scoring his side's third and final goal.
The 22-year-old had been isolated from the squad due to being infected with the mumps.
"But I had faith and courage ... my thinking was I would get on the field and play," he said.
"I put it in my head that it would heal quickly. Every morning when I woke, I went straight to the mirror to see if the lump had diminished."
Richarlison said he had dedicated his goal in the 90th minute to his great-grandfather, adding on cbf.com.br: "It was a moment that will remain forever in my memory."
The win was built from a solid platform of team cohesiveness, midfielder Casemiro said after the match.
"Winning a title with the Selecao is any child's dream.
"This is an important title, I'm very happy, it will undoubtedly become a very special memory for me.
"The key to all this was to have a solid team," the 27-year-old added.