Venezuela, no longer the whipping boys of South American football, took their first ever points in 19 qualifiers against Argentina when central defender Fernando Amorebieta headed the only goal from a Juan Arango corner just past the hour.
"In these qualifiers we're going full out, this is an historic night and we must enjoy it," Venezuela captain Arango told reporters.
Goalkeeper Mariano Andujar make several good saves to keep the score down for a surprisingly lacklustre Argentina, who had thrashed Chile 4-1 in Buenos Aires on Friday with a Gonzalo Higuain hat-trick and a goal from the talismanic Lionel Messi.
Venezuela coach Cesar Farias could also feel vindicated after he was criticised for resting key players in the 2-0 loss against Ecuador in Quito on Friday.
The only team in the 10-nation South American Football Confederation never to have qualified for the finals, Venezuela have emerged as serious contenders for a place in Brazil after their fourth place at the Copa America in Argentina in July.
It was a first defeat for Argentina's new coach Alejandro Sabella, who took charge in August after Sergio Batista was sacked following his team's quarter-final defeat to Uruguay in that tournament.
"We were superior for the first 25 minutes but we came up against a well-prepared Venezuela," Sabella told reporters.
Experienced in the marathon South American qualifying campaign having assisted Daniel Passarella with the Argentina team that reached the 1998 quarter-finals in France, Sabella added: "It's a long, hard road. We'll try to work hard to overcome what happened today."
