Venezuela got the opening goal against Argentina just four minutes into the second half, when Jhon Murillo ran onto an incisive through ball and expertly chipped the advancing goalkeeper to give the visitors a surprise lead. The advantage, though, lasted just four minutes when a cross was knocked into his own goal by Rolf Feltscher.
Mauro Icardi had a good shout for a penalty waved away after an hour but Argentina, with Lionel Messi not at his commanding best, looked lacklustre throughout and were unable to stamp their authority on the match.
Neither they nor Venezuela created many clear-cut chances and the home side trooped off to the boos of their disgruntled fans.
Brazil top the 10-team group and are the only South American side so far to have qualified for Russia 2018. They drew 1-1 with Colombia in a hard-fought qualifier after Radamel Falcao's second-half header cancelled out Willian's stunning first-half volley.
Colombia have still never beaten Brazil in a World Cup qualifying match but the draw marked the first time in 10 games that Brazilian coach Tite has come away from a qualifier with anything other than all three points.
Uruguay, who won 2-1 away at Paraguay, are in second-place with 27 points, followed by Colombia on 26. Peru, who have not played in the World Cup Finals since 1982, beat Ecuador 2-1 earlier in the evening to move into fourth place with 24 points, ahead of Argentina on goal difference.