The 31-year-old, who recently joined Saudi side Al-Hilal, bounced back after missing a penalty in the first half by scoring two goals in the 61st and 93rd minutes to become the country's all-time top scorer on 79 goals.
“Congratulations Neymar for surpassing the King in goals for Brazil,” the official account of the late Brazil soccer legend Pele wrote on X, the platform formerly called Twitter. “Surely Pele is applauding you today!”
Neymar said after the game: “I never imagined reaching this record.
“I want to say that I am not a better player than Pele. I always wanted to make my own story, write my name in the history of Brazilian football and the national team. And today I did that.”
Neymar has played 125 times for Brazil and was part of the team that won the Confederations Cup in 2013.
Real Madrid's Rodrygo also shone with a double, opening the scoring in the 24th minute and bagging his second in the 52nd off a great through ball from Newcastle midfielder Bruno Guimaraes for 3-0.
“It really is a very special day... Neymar is my idol, being able to help him become the top scorer will stay with me forever,” the 22-year-old Rodrygo told Brazilian broadcaster TV Globo.
Raphinha, who replaced Antony in the Brazilian squad, scored to make it 2-0 in the opening seconds of the second half with a shot at the far post after picking up Neymar's pass in the edge of the box. Bolivia got their consolation goal through Victor Abrego's powerful shot in the 78th minute.
Brazil will look to continue their good form when they visit Peru on Tuesday in the second round of CONMEBOL qualifiers.
Elsewhere, Uruguay started their qualifying campaign on the right foot by beating Chile 3-1 at home to hand former Leeds coach Marcelo Bielsa his first official win at the helm.
Additional reporting by Reuters.