The Pumas scored classy tries through Joaquin Tuculet and Juan Manuel Leguizamon and led 23-13 at one stage. But second-half tries from Bryan Habana and Pieter-Steph du Toit, and two penalties from Morne Steyn edged the Springboks in front before Argentina responded with the match winner three minutes from time.
The Pumas head to London to take on Australia on October 8 in the final round of The Rugby Championship – the first time the tournament has come to Europe.
Tickets to Argentina v Australia at Twickenham Stadium are available from £45 for adults, £25 for children (U16) and a family package (2 adults & 2 children) for £115. (Booking fees apply.) Click here for details.