Argentina were behind as early as the sixth minute courtesy of a well-worked execution from Newcastle United striker Salomón Rondón.
The Albiceleste soon opened up, but Lautaro Martinez failed to finish off a well-worked move after rounding Wuilker Farinez at the midway point.
The Argentines left a lot of space at the back and were almost caught out by Darwin Machis who failed to beat Francesco Armani in a one-on-one scenario after 36 minutes.
Despite Argentina's dominance, Venezuela added to their tally a minute to halftime following a stunning finish from Jhon Murillo.
The two-time World champions attempted a comeback, as a timeous run from Martinez ended with an emphatic finish past Farinez on 59 minutes.
The Venezuelans made the game’s first change in Yeferson Soteldo for Yangel Herrera on 66 minutes with Josef Martinez replacing Rondon shortly thereafter.
Argentina’s road to a comeback took another twist after Venezuela received a penalty for a foul by Machis with 15 minutes remaining, leaving Martinez to restore their two-goal advantage from 12-yards out.
Argentina threatened once more just before full-time, but Dario Benedetto’s header off Messi’s cross sailed wide of the post as Venezuela hung on for a famous win in Madrid.