Venezuela had never beaten Brazil in a World Cup qualifier in 17 previous attempts but their hopes rose after taking an early lead through Eric Ramirez, who converted Yeferson Soteldo's cross after defenders Fabinho and Marquinhos slipped at the vital moment.
However, Brazil got back on level terms when Marquinhos headed home a corner in the 71st minute before Gabriel Barbosa scored a penalty six minutes from time and Anthony made it 3-1 in stoppage time.
With Argentina's 0-0 draw at Paraguay, Brazil extended their lead at the top of the South American qualifying group to eight points. The top four teams qualify automatically for Qatar and the fifth-placed side goes into an inter-regional playoff.
However, it was the introduction of second-half substitutes that turned the game for the five-times world champions.
Leeds United's debutant Raphinha opened up space and hit the corner that led to Marquinhos' goal, while Vinicius Jr. was instrumental in the buildup that led to Barbosa's penalty.
Raphinha also set up fellow substitute Anthony to tap home just before the final whistle.