Bolivia went 2-0 ahead in less than half an hour when Alejandro Cichero headed into his own net and Jose Castillo scored his third goal of the qualifiers.
Giancarlo Maldonado pulled one back after halftime but substitute Joselito Vaca restored Bolivia's two goal advantage late in the game.
Venezuela are sixth in the 10-nation group, level on 14 points with Colombia and Chile, while Bolivia climb above Peru although both teams have 13 points.
Venezuela, already missing six players through injury and suspension, made a nightmare start when Cichero met Gonzalo Galindo's header with a diving header which flew past goalkeeper Rafael Dudamel and into his own net.
Giancarlo Maldonado wasted an excellent chance for a quick reply three minutes later when he charged down Oscar Sanchez's attempted clearance, burst through the Bolivia defence but fired wide.
Castillo increased Bolivia's lead in the 26th minute when he played a one-two with Vaca, slipped past Cichero's lunging challenge and fired the ball into the roof of the net.
Venezuela replaced Cichero with striker Daniel Noriega at halftime and pulled one back in the 71st minute when the ball fell kindly for Maldonado to score from the edge of the area.
Vaca, who replaced the injured Ronald Garcia in the 21st minute, swept home the third to give Bolivia their first win under coach Ovidio Messa with six minutes left.
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