Juan Carlos Arce's stunning 87th-minute effort gave Bolivia their first win since February 2013.
Goals from Ronald Raldes and Damian Lizio had put them on track after Wilker Angel's opener for Venezuela in La Paz.
But Alexander Gonzalez scored a 71st-minute equaliser for the visitors, who are winless since September last year, before Arce's late effort.
Noel Sanvicente made four changes to the starting Venezuela side that were beaten 5-0 by Chile on Friday as he looked for his first win since taking charge in July.
Nestor Clausen was at the helm for one game for Bolivia due to interim coach Mauricio Soria being suspended.
And his team - in action for the first time since October - started well with Carlos Saucedo causing plenty of problems.
But the visitors went close in the 11th minute as Juan Arango curled a 30-yard free-kick just over the bar.
Unsurprisingly, the best early chance fell to Saucedo.
The 35-year-old striker was left unmarked in the middle of the area, but he headed a corner well over.
Venezuela were inches away from taking the lead in the 26th minute through Luis Manuel Seijas.
The midfielder's powerful 30-yard strike had Romel Quinonez beaten, but it crashed off the crossbar.
And six minutes before half time Venezuela went ahead through debutant Angel, who guided in an Arango set piece with the faintest of touches.
It was an entertaining end to the half, with Bolivia levelling in the 41st minute.
Raldes attacked Lizio's corner and headed into the top corner for his first international goal.
Both teams had chances in an action-packed end to the half, but the teams deservedly went into the break locked at 1-1.
Bolivia were on track to end their miserable run of form when Lizio put them ahead in the 53rd minute.
Miguel Hurtado, in plenty of space, whipped in a cross from the right and Lizio guided a smart header into the far corner.
Gonzalez got Venezuela back on level terms in the 71st minute, taking down Romulo Otero's pass with his chest before firing into the roof of the net at the near post.
Saucedo had the ball in the net eight minutes later, but he was correctly ruled offside.
But Arce delivered when Bolivia needed it most, cutting inside from the left before powering a 25-yard effort into the top corner.