The tournament hosts were far too good for Ricardo Gareca's side at Arena Corinthians on Saturday, scoring three goals in the first half and extending their run of Copa clean sheets.
Casemiro's first Brazil goal opened the scoring and Roberto Firmino quickly made it 2-0, with Everton's superb drive adding to the Selecao's lead before the break. Captain Dani Alves and Willian scored fine goals after the interval before Gabriel Jesus saw a late penalty saved.
The next opponents for Tite's side will be set when Groups B and C conclude, while Peru must wait for other results to see if finishing third behind Venezuelais enough to see them through.
Brazil bundled in an untidy opening goal in the 12th minute when Peru failed to defend a Philippe Coutinho corner from the left wing.
Marquinhos somehow headed against the inside of the post from point-blank range and was fortunate the ball bounced up perfectly for Casemiro to make sure, with Brazil soon doubling their lead with a similarly strange goal.
Firmino charged down a clearance from goalkeeper Pedro Gallese and appeared to celebrate prematurely before the ball rebounded off the post, but the Liverpool forward recovered his composure to round the goalkeeper and slot into the open goal with a trademark no-look finish.
Everton, who impressed off the bench in Brazil's first two games, made it 3-0 before the break with a drilled 20-yard finish after cutting in off the left wing.
Brazil hit top gear with a brilliant fourth goal in the 53rd minute. Barcelonamidfielder Arthur was heavily involved in the build-up before Alves swapped passes with Firmino and smashed his finish home.
Coutinho's fine performance was rewarded with warm applause when he was substituted in the closing stages, his replacement Willian curling in an unstoppable fifth.
And Gallese salvaged some pride in added time by denying Jesus from the penalty spot after bringing down the Brazil forward.
Brazil recapture rhythm at last
After toiling in their opening two Copa matches Tite's side found fluency, albeit against a poor Peru outfit few would have guessed had taken four points from their Copa campaign.
The Selecao - brushing off pre-match accusations Tite had spied on Peru training with a drone - looked more balanced and clinical in the final third, which bodes well for the last eight.
