Pizarro scored in the 12th minute when he controlled midfielder Juan Vargas's cross with his back to goal and sent an overhead kick inside the far post.
The victory saw Peru climb above Uruguay into sixth place with 14 points from 11 matches.
The top four teams at the end of the qualifiers in October will go through to the World Cup finals in Brazil, while the fifth-placed team will enter a play-off against an Asian qualifier in November for another berth.
Venezuela are currently in fifth position with 16 points from 12 games.
Peru were indebted to goalkeeper Raul Fernandez, who kept out a goal-bound deflection from defender Alberto Rodriguez and saved Ecuador striker Felipe Caicedo's header from the edge of the six-yard box.
Pizarro, the team's captain, also helped out in defence, clearing off the line in the first half.
Peru had the ball in the net again early in the second half but Jefferson Farfan's effort was ruled offside.