Uruguay's 2-0 win over Colombia meant the hosts at Puerto la Cruz needed to win their final two games to be any chance of sneaking into the South America qualifying play-off spot.
And things went even more awry early when Peru took a lead against the run of play, when Paolo Hurtado completed a fine run with a powerful strike from the right past the on-rushing Venezuela goalkeeper Daniel Hernandez on 20 minutes.
But the home side responded well, taking control of the contest at least in general play and creating numerous chances before Salomon Rondon converted with a sharp right-foot stab past Peru keeper Raul Fernandez eight minutes before half-time.
The goal dashed Peru's hopes of keeping a clean sheet, although that was already looking unlikely, after Fernandez had earlier tried to clear a ball by punching, only for the ball to go backwards and only just fly over the crossbar.
The sides were level at the interval but it was all Venezuela from there onwards with Yohandry Orozco forcing a save out of Fernandez in the 46th minute to signal the hosts' intentions.
A 62nd-minute penalty then shattered Peru's hopes of a comeback, as Cesar Gonzalez confidently stepped up with a well-taken spot kick to put Venezuela ahead. Carlos Zambrano had conceded the penalty when he handballed in the area.
Romulo Otero then wrapped up the three points with a delightful low strike from the edge of the area, with the right-foot shot to the bottom right corner needing to be inch perfect to beat a diving Fernandez.
It was deserved reward for Venezuela, who looked the only team likely to score after the two sides emerged from the dressing rooms.
Zambrano tried to atone for conceding the spot kick, when he pulled a goal back in the shadows of the final whistle but it would not be enough to salvage a point for Peru.
The win leaves Venezuela three points behind Uruguay, who have a game in hand.
The former would need to win their final fixture against Paraguay and hope the Uruguayans lose to both Ecuador and Argentina, all the while making up a differential of six goals.
Peru's qualifying hopes were slim prior to kickoff and the loss extinguished any chance they could reach fifth place, ensuring their Brazil dream is officially over.
