A second-half own goal from Venezuela defender Rolf Feltscher spared Argentina’s blushes after the visitors had taken the lead through Jhon Murillo.
The result left Argentina in fifth place in the South American standings with 24 points from 16 games.
The top four finishers in the table qualify for next year’s final automatically, while the fifth place team faces a two-leg playoff against New Zealand.
Argentina would still be favourites to progress to Russia past the New Zealanders, but will be taking nothing for granted in their final two qualifiers next month after another disjointed performance.
Venezuela, bottom of the table and already eliminated from contention, more than held their own for long periods as Argentina struggled to click despite a star-studded line-up spearheaded by Lionel Messi, Mauro Icardi and Paulo Dybala.
After a lacklustre first half display, Venezuela took a deserved lead six-minutes into the second half with a sweeping counter-attack that exposed Argentina.
A flowing move ended when Sergio Cordova threaded a perfect pass through to Murillo who deftly tucked his finish past Manchester United’s Sergio Romero.
However Argentina got back on level terms three minutes later when substitute Marcos Acuna sprinted down the left before crossing into the six-yard area.
Under pressure from Icardi, Feltscher turned the ball into his own net.
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