Venezuela, who are looking to reach the finals for the first time, went in front when midfielder Juan Arango headed home Richard Blanco's flick-on from a Cesar Gonzalez corner in the 58th minute.
But substitute Jhasmany Campos headed home an 86th minute corner to salvage a 1-1 for the Bolivians at the Hernando Siles stadium, a result that suited neither side.
Venezuela move a point ahead of Chile, who are away to Paraguay later, into fourth place ahead of Tuesday's home clash with sixth-placed Uruguay.
Bolivia remain one from bottom of the standings with little chance of reaching next year's finals in Brazil.
The top four teams at the end of the qualifiers in October will go through to the Brazil finals. The fifth-placed team will enter a play-off against an Asian qualifier in November for another berth.
- Sports & Recreation
- Juan Arango
- Richard Blanco