The tournament host was far too good for Ricardo Gareca's side, scoring three goals in the first half and extending its 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 opponent 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 Venezuela, which beat Bolivia 3-1 in their match, is enough to see it 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 its 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. Barcelona midfielder 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.
Gallese then salvaged some Peru pride in stoppage-time by denying Jesus from the penalty spot after bringing down the Brazil forward.
After toiling in its opening two Copa America matches, Tite's side found fluency in this final group clash, albeit against a poor Peru outfit few would have guessed had taken four points from its own 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.