Stellenbosch had another chance to equalise late in the second half, but Ivorian substitute Anicet Oura headed wide from close range.
Victory took Sundowns to 72 points — a Premiership record — with matches to come against TS Galaxy (away) and Cape Town City (home) next week.
If they avoid defeat in those two fixtures, they will be the first club to complete a season unbeaten since the league launched in 1996.
Despite losing a second successive match, Stellenbosch stayed second, one point ahead of Orlando Pirates, in the race to finish runners-up and qualify for the CAF Champions League.
For the second weekend in a row, former African champions Pirates failed to take advantage of Stellenbosch losing.
Pirates were beaten 1-0 at TS Galaxy, whose winner from Sphiwe Mahlangu came midway through the second half in northeastern city Mbombela.
Galaxy rose to fourth, and if they retain that position after the final round next Saturday will enter the CAF Confederation Cup, the African equivalent of the UEFA Europa League.
Regular African campaigners SuperSport United are also contenders for a CAF Cup spot. They trail Galaxy on goal difference after a 2-0 home win over lowly Moroka Swallows near Pretoria.
While Cape Town Spurs have been automatically relegated, who finishes second last and goes into play-offs with two second division clubs remains uncertain.
Third-from-bottom Royal AM snapped a five-defeat run by holding visiting Chippa United 0-0 and are three points above Richards Bay, who fell 3-1 at Cape Town City.
© Agence France-Presse
Photo: Twitter @Masandawana