The home side had won all six of their previous home qualifiers against Venezuela and were expected to do the same against the team that is bottom of the South American group and without a win in 10 games.
Argentina's failure to take all three points left them fifth in the standings with two matches remaining, out of the top four spots which bring with them direct qualification for the finals.
Venezuela are well out of the running but got the opening goal just four minutes into the second half.
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 and when Argentina equalized it came from the same left flank where all of their most dangerous attacks originated.
Marcos Acuna, who had replaced the injured Angel Di Maria after 25 minutes, fought off his marker and the 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 America side to have so far qualified for Russia 2018.
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.
The fifth-placed side go into an intercontinental playoff against New Zealand.
(Writing by Andrew Downie, editing by Nick Mulvenney)
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