The five times world champions scored nine goals in their last two games but they struggled from the start against a resilient Venezuela, the only one of the 10 South American sides never to have qualified for the World Cup finals.
Richarlison had Brazil ahead in the seventh minute only for the goal to be chalked off for offside and the same player's foul on the keeper caused a second from Douglas Luiz to be ruled out five minutes before half time.
The winner eventually came from Firmino midway through the second half when he was well-placed to push the ball home from close range after a defensive header fell at his feet.
"We were able to compete and do them damage for a while," said Venezuelan midfielder Luis Mago. "We made one mistake and paid a heavy price for it."
The win means Brazil have nine points from nine. They have not lost a World Cup qualifier since a 2-0 loss to Chile in 2015, 20 games ago.
The result leaves them top of the South American qualifying group after three games, while Venezuela, the only one of the 10 South American teams yet to score a goal, languish joint second bottom with Peru, with just one point.
Bolivia are the only pointless team after three matches.
The top four sides in the 10-team group qualify automatically for the finals in Qatar in 2022 and the fifth-placed team go into an inter-regional playoff.
Brazil's next game is away to Uruguay on Tuesday, while Venezuela are at home to Chile the same day.