Brazil had been jeered by its own fans in its opening two pool matches – a 3-0 win over Bolivia and 0-0 draw with Venezuela – but it was all cheers in Sao Paulo as it secured top spot, AFP reported.
"We were creative, precise, clinical and effective," enthused Tite.
"It was one of the best" matches during his reign in terms of keeping the ball and getting in behind the defense, he added.
And he recognized that it was the Selecao's fast start that made the difference, taking the lead after just 12 minutes through Casemiro.
"Since we scored in the first half we had to maintain that tempo," he said.
"We kept the same attitude and we were still creating chances in the 47th minute of the second half."
The game was over as a contest by halftime after further goals from Roberto Firmino and Everton.
A Dani Alves strike early in the second half piled more misery on Peru and even after Willian scored in the last minute, Gabriel Jesus won a stoppage time penalty.
Peru goalkeeper Pedro Gallese made amends for giving it away by saving Jesus's spot-kick.
"We carried on creating chances even at 5-0," said assistant coach Cleber Xavier.
Captain Alves said Brazil improved in every match during the pool stage.
"We're improving: From the first to the second, to the third match," said the Paris Saint-Germain fullback.
The manner of victory also allowed Brazil to get back in the good books of a notoriously demanding public.
The Brazilians were jeered at halftime against Bolivia in a match they went on to win 3-0. And the boo-boys were back for their goalless stalemate with Venezuela.
"When you manage to score a goal, it calms you down and gives you continuity for the rest of the match," said Alves.
"And when the goal doesn't come, it seems to create anxiety."
For Peru, it now faces a tense wait to find out if it will make it into the knockout stages.
Venezuela leapfrogged Peru with a 3-1 win over Bolivia and Peru is now hoping to finish as one of the two best third-placed teams.
Jefferson Farfan said "it was one of the toughest" matches of his life, but worse still for goalkeeper Pedro Gallese, whose horror gaffe cost Peru the second goal.
He was also partially at fault for the first and third and gave away the late penalty.
"The whole team spoke with Gallese, he's calm, he has everyone's support," said Farfan.
"Obviously we all made mistakes. Everyone played badly today."