The fly-half claimed three
tries and kicked eight conversions and two penalties for South Africa, who lead New Zealand by one point with one round remaining.
His points haul bettered by two the 35 of retired full-back Percy Montgomery for the Springboks against Namibia.
Flanker Pieter-Steph du Toit scored two tries for the home team, who dominated the second half after leading 25-23 at halftime.
Other try scorers for South Africa were hooker Malcolm Marx, winger Cheslin Kolbe, halfback Morne van den Berg and substitute back Manie Libbok.
Argentina fly-half Santiago Carreras slotted three penalties and two conversions, centre Santiago Chocobares and substitute back Tomas Albornoz scored tries. The Pumas were also awarded a penalty try.
Argentina twice led by five points in a first half that came alive in the closing stages after the early exchanges were dominated by penalties and box kicks.
South Africa suffered a double blow just before half-time when they conceded a penalty try, and Marx was yellow-carded for his role in a collapsed maul that led to it.
But the Springboks still had time for Feinberg-Mngomezulu to score his second try and convert it for a two-point advantage at the break.
After a close, tense, opening half, South Africa took control to score a further six tries as the Pumas resistance crumbled under constant pressure.
South Africa have 15 points after five rounds, New Zealand 14, Australia 11 and eliminated Argentina nine ahead of the final matches on October 4.
The Wallabies host the All Blacks in Perth, then the Pumas will face the Springboks again, in a match to be staged in London for commercial reasons.