Mahmudullah and Liton Das (18) put on 43 after lunch, but the latter's decision to play no stroke to one from Andile Phehlukwayo (3 for 36) saw his off stump uprooted.
Ironically Mustafizur was replaced by Subashis Roy and when Elgar hooked again, Mustafizur ran in from fine leg to take a fine diving catch for Bangladesh's only success before tea.
It was that kind of a Test with nothing going right for Bangladesh and their struggle against pace and bounce was very apparent as they were bundled out for 172 in the second innings.
Bangladesh was all out for 147 in its first innings on day two in reply to South Africa's 573-4 declared.
Bangladesh couldn't bowl the Proteas out in any of the three innings over the two Tests, with the home batsmen cashing in after a hard tour to England. In the absence of a doctor in the Bangladesh camp, South African team manager Mohammad Moosajee, who is a medical doctor, advised Mushfiqur to leave the field for further inspection. So, Proteas came to bat with their top two openers Elgar and Markram.
Neither did though - in Elgar's case it's simply not his way - while Markram, for all his attacking intent, was especially watchful here, seeking to atone for missing out on the landmark in his debut Test last week. When he reached 16 he became the first batsman in the world to score 1000 runs in 2017.
Du Plessis continued: "We had really good targets that we wanted to achieve in this series and we achieved those hands down".
It took the hosts just the three days to wrap up the Test.
Rabada, however, showed there was life in the wicket as he turned in a virtuoso display. They took 20 wickets conceding just 319 runs, an average of just 15.95 runs per wicket.
Adding to the tourists' woes, Elgar was also dropped on 110 by wicket-keeper Liton Das, a hard chance that came his way when Elgar misjudged a pull off Mustafizur, with the ball looping high towards Das. Olivier, however, put an end to Kayes' resistance by cramping him down the leg-side with a short ball that took a thick edge on its way to the keeper.