Fernando Amorebieta was the hero for the Vinotinto as Cesar Farias' side defeated the Albiceleste for the first time in their history. The result saw Venezuela bounce back in style after suffering a 2-0 defeat by Ecuador in their opening qualifying clash at the weekend.
Venezuela attacked Argentina throughout and the return of midfielder Javier Mascherano and defender Martin Demichelis in Argentina's line-up was not enough as Lionel Messi and Gonzalo Higuain under-performed in Puerto La Cruz.
The only goal of the game came in the 61st minute, when Athletic Bilbao defender Amorebieta headed the ball into the back of the net after a corner by Juan Arango.
Earlier, Argentina keeper Mariano Andujar was the key figure. In the first half, he saved a superb free-kick by Arango while the Catania custodian also stopped an Arango shot in the second period.
Argentina boss Alejandro Sabella told a post-match media conference: "We have to analyse what we should improve. The qualifiers are a long tournament and we must improve some aspects.
Venezuela defender Oswaldo Vizcarrondo told Argentinian Channel 7 that they have to go step-by-step towards the dream of a maiden FIFA World Cup appearance: "We have to keep our feet on the ground. We dream about the World Cup. In the Copa America earlier this year, it was a matter of seizing the moment. Now, we have to keep ourselves at a good level for three years."
Midfielder Cesar Gonzalez added: "We made history. We brought our soul on the field. We are family. We back the coach and each other. The goal is the World Cup. We defeated a big team, but there is a long, long way to go."