An interception try five minutes from time handed Argentina the winning score to deny Worcester victory at Sixways.
The Pumas, who open their World Cup campaign next month against England, edged home against battling Warriors.
Fly-half Joe Carlisle claimed all Warriors' points with his boot before a mistake from Sione Tu'ipulotu allowed the Pumas in for their vital, late try.
Wing Juan Imhoff broke away, adding to his earlier try when the cover defence failed to stop him in the corner.
Warriors coach Richard Hill told BBC Hereford & Worcester:
"We took a huge amount from it in attack and defence.
"We looked very sharp and their defence prevented us scoring a few tries."
"The confidence we will get from these games is massive, although the talk after the game was good as they were disappointed to haver lost."