The hosts dominated in Buenos Aires, but remarkably fell behind early in the second half when Jhon Murillo struck for Venezuela.
Venezuela, bottom of the CONMEBOL table, had been on the back foot throughout, and Argentina managed a quick response through a Rolf Feltscher own goal.
But Jorge Sampaoli's men were unable to find a second, having frustratingly been denied throughout the first half by Venezuela goalkeeper Wuilker Farinez.
A hamstring injury to Angel Di Maria in the first half made it even trickier, while Lionel Messi was unable to have a major impact.
The draw was enough to at least lift Argentina into fifth – the play-off spot – heading into the final two matches in October.
Sampaoli made three changes to the starting side held in Uruguay, with Javier Mascherano, Ever Banega and Lautaro Acosta replacing Gabriel Mercado, Lucas Biglia and Marcos Acuna.
Also coming off a 0-0 draw – theirs against Colombia – Venezuela coach Rafael Dudamel brought in Arquimedes Figuera, Junior Moreno and Murillo for Tomas Rincon, Josef Martinez and Darwin Machis.
Argentina made a superb start in front of a vocal home crowd, almost taking a fourth-minute lead.
Mascherano played a fine pass through for Mauro Icardi, who was denied by the legs of Farinez in a one-on-one.
The hosts continued to push, with Di Maria particularly lively down the left as an opener appeared certain to arrive.
It almost came midway through the first half, but Farinez brilliantly denied Icardi after the Inter forward got on the end of a Di Maria cross.
In a huge blow, Argentina lost Di Maria to an apparent hamstring injury in the 25th minute, before Paulo Dybala fired wide.
Farinez was called into action again just before the break, the 19-year-old diving to his right to push away a 20-yard effort from Messi.
Argentina had dominated, but they stunningly fell behind in the 50th minute.
A blistering counter-attack led to Murillo being put through by Sergio Cordova, and the 21-year-old made no mistake with a fine finish to give his side a shock lead.
Argentina needed a quick response and they got it, Acuna – Di Maria's replacement – doing brilliantly down the left before his cross was turned into his own net by Feltscher.
Icardi then appeared to be brought down by Mikel Villanueva in the area on the hour-mark, but penalty shouts were rejected.
The hosts continued to push for a winner, but their final pass continually let them down as Venezuela held on for a shock draw.