Two second half goals, Manchester City-bound Gabriel Jesus scoring the first and setting up the second for Renato Augusto, gave Brazil the points in Lima against a home team that played well for no reward.
"I am working hard, quietly, hoping to help my team mates on the pitch," the 19-year old striker told TV Globo after the game.
"There are lot of players in Brazil who can wear the No. 9 but I am proud that I have this opportunity. I am proud to be honouring the shirt."
Peru had never beaten Brazil in 10 previous World Cup qualifying matches but they took the game to their more illustrious visitors and were unlucky to come up against two clinical finishers.
The Palmeiras forward, who will join Manchester City in January, got the first 12 minutes into the second half when the ball fell kindly to him to hammer home from 13 yards.
He turned provider 21 minutes later, laying the ball off to Renato Augusto in space and the Beijing Guoan midfielder made no mistake from 12 yards.
The result was a trifle harsh on Peru, who hit the post early on and were not overawed, particularly in an even first half.
The result marked the first time since 1969 that Brazil have won six consecutive qualifying matches for the same tournament.
Brazil now lead the table with 27 points from 12 games, four more than second-placed Uruguay.
The top four teams qualify automatically for Russia 2018 and the fifth-placed side goes into a play-off with a team from Oceania.
In the day's earlier games, Ecuador beat Venezuela 3-0 to stay in third, while a late own goal from Gustavo Gomez gave Bolivia a 1-0 win over Paraguay in La Paz.
Chile beat Uruguay 3-1 to climb into fourth spot, and Argentina, with a beautiful free kick from Lionel Messi, beat Colombia 3-0 to snap a four-game winless streak and move into fifth place.
(Writing by Andrew Downie; Editing by Andrew Both)
