The South Africans will face Australia in a last-eight round fixture on Sunday, after the men from Down Under finished second to the USA in Pool D.
Against Argentina, the SA side scored first for the third time in as many matches, with skipper Siviwe Soyizwapi going over the Argentinian tryline in the thirrd minute.
The consistent boot of Branco du Preez added the conversion to make the score 7-0.
However, the South Americans took the game to the Blitzbokke and were rewarded with a five pointer in the fifth minute when German Schulz scored with Lautaro Bazan Velez slotting the conversion to level the scores at 7-all.
The speed of Kurt-Lee Arendse has been one of the highlights of the tournament and he was on hand to finish off a move that, with the conversion from du Preez, allowed the Blitzbokke to move into a 14-7 lead.
With the halftime hooters having sounded, Soyizwapi went over for his second try of the half, with the conversion of Du Preez, allowing the Blitzbokke to hold a 21-7 lead at the break.
Any hopes that the Argentinians had of stunning the Blitzbokke early in the second half, fell by the wayside as superb offloads saw Stedman Gans and Muller du Plessis run in tries, with Selvyn Davids converting one to take the scoreline to 33-7.
Gaston Revol and Francisco Ulloa managed to breach the Blitzbokke defence in the 12th and 13th minutes respectively, to bring the Argentinians back to a more respectable 21-33 deficit.
However, it was the ever-present Werner Kok who had the last say as he outwitted the opposing defence with his usual mix of class, speed and strength with some fine stepping added in, to dot down.
Davids converted to allow his team to hit the 40-point mark for the third time in as many matches.
Earlier on Saturday, the Blitzbokke thrashed Japan 49-0 before posting a 45-14 win over Canada.
- African News Agency (ANA)