Having dominated much of the opening exchanges, Venezuela suffered a major setback when defender Fernando Amorebieta was sent off for a deliberate stamp on Paolo Guerrero after just 30 minutes.
Despite their numerical advantage, Peru struggled to break Venezuela down, and it was only in the final quarter that they opened the scoring.
Pizarro eventually did so in emphatic fashion, the Bayern Munich man smashing a Guerrero ball into the back of the net via the underside of the bar after keeper Alain Baroja got fingertips to his effort.
The result means that there is a logjam in Group C with all four teams level on three points after two fixtures.
In the final round of Group C matches on Sunday, Colombia play Peru while Brazil face. Venezuela.