Bayern Munich's Pizarro scored on a left-footed shot that was tipped by Venezuela goalkeeper Alain Baroja but still went in off the underside of the crossbar.Venezuela, which upset Colombia in its opening match, was in command until defender Fernando Amorebieta was sent off on a straight red card in the 29th for stomping on the leg of Peru's Paolo Guerrero.
All four teams in Group C have three points after two matches: Brazil, Peru, Venezuela and Colombia.
Venezuela controlled the early play as Peru had trouble getting out of its own end. Venezuela's Salomon Rondon was in alone in the 7th but shot directly at keeper Pedro Gallese. Teammate Alejandro Guerra also had early chances.
The sending off of Amorebieta by referee Raul Orosco changed the complexion. There is no doubt Amorebieta stomped on Guerrero, but it was not clear it was intentional.
That turned the heat up and changed the match, though even with the extra man Peru mounted little sustained attack in the first half.
Peru's attack threatened early in the second half with Pizarro and Guerrero looping early headers over the crossbar.
After Pizarro scored, Peru kept more possession and was successfully running time off the clock as Venezuela never really threatened.
On Sunday in the final Group C match, Colombia plays Peru and Brazil faces Venezuela.
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