Brazil, who crushed Bolivia 5-1 at home on Friday, moved level on six points with rivals Argentina at the top of the South American qualifying standings.
Interim coach Fernando Diniz's side dominated possession and attacking opportunities early in the game but Raphinha and Richarlison saw goals ruled out for offside in the first half.
"I'm pleased with what we've shown in both games. Today's game was a different atmosphere. The team had to score three goals to make one count," Diniz told reporters.
"It's always important to win. I think we won with a lot of credit. I really enjoyed it."
With the game heading towards a scoreless draw Paris St Germain defender Marquinhos headed home Neymar's corner at the near post to seal the win in the 90th minute.
"We practised set pieces both in Belem and here. Set pieces define the game, today it did," Diniz added.
"We scored through persistence. A well struck ball and anticipation on the first post."
The five-times world champions will host Venezuela before visiting Uruguay next month when qualifying continues.
In other qualifiers earlier on Tuesday, Argentina cruised past Bolivia 3-0, Venezuela beat 1-0 Paraguay, Uruguay lost 2-1 at Ecuador, while Chile and Colombia drew 0-0.
