The Pumas were nearly kept tryless for the second straight playoff match, before replacement Juan Pablo Orlandi crashed over with the final play of the game.
The Springboks wing JP Pietersen opened the scoring early on in the right corner and they led 16-3 at half-time, before lock Eben Etsebeth added the Boks' second try in the left corner.
Pumas openside flanker Juan Martin Fernandez Lobbe played his final Test match in the fixture, as did South African wing Bryan Habana and lock Victor Matfield - the oldest Springbok ever at 38.
Habana needed just one try to overtake Jonah Lomu's all-time World Cup record at the tournament.
Their team-mates Schalk Burger and Fourie du Preez are expected to retire from international rugby now too.