The draw put hosts Peru, who had four points as they went into their final match against qualified group A leaders Colombia later on Monday night, through to the second round.
Bolivia need Chile and Costa Rica to draw 0-0 or 1-1 in their final group C match on Wednesday to reach the last eight.
Venezuelan striker Ruberth Moran put the "Red Wines" into the lead with a goal in the 27th minute, knocking in the ball from six metres after Bolivian keeper Leonardo Fernandez was unable to hold onto a fierce shot from Richard Paez.
The goal kick-started Bolivia into life and a period of pressure bore fruit when midfielder Gonzalo Galindo's low drive found its way through the Venezuelan defence into the bottom left-hand corner from the edge of the area in the 33rd minute.
Bolivia almost took the lead six minutes later when Limberg Gutierrez struck a curling free kick that looked sure to go in to the top left corner, but Venezuelan keeper Gilberto Angelucci responded to tip the ball over brilliantly.
Gutierrez tested Angelucci again three minutes later with another free kick from the left, but Angelucci was able to force a corner.
Bolivia, who were without their injured captain Luis Cristaldo, a veteran of Bolivia's 1994 World Cup team, also lost Limbert Pizarro in the 16th minute to injury.
Venezuela were unlucky not to take the lead in the second half, pouring forward with stylish passing moves and putting a handful of shots on goal.
Substitute Alex Rondon hit the post in the 75th minute with a low shot from the left and Fernandez put on a spectacular display to keep out Rondon's shots right into injury time.
Bolivia were dangerous on the counter-attack and Roger Suarez missed several good chances, too often putting the ball into the hands of Angelucci.
Venezuela go out of the tournament with two losses and a draw, unable to notch up their first Copa win since 1967 despite their recent good form in the World Cup qualifiers.
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