Bangladesh were 92 for four at lunch at the Mangaung Oval in their follow-on, still trailing South Africa by 334 runs, with captain Mushfiqur Rahim out the last ball before the interval for 26 as he was trapped leg before wicket by Wayne Parnell.
Rabada had snagged Soumya Sarkar and Mominul Haque in the first hour on Sunday to take his test career tally to 99, and Imrul Kayes was then caught behind off Duanne Olivier for 32.
Rabada took five wickets in the first innings as Bangladesh were bundled out for 147 and then forced to follow-on, scoring seven without loss before bad light stopped play on Saturday.
South Africa amassed 573-4 declared in their first innings and require six wickets for victory to take the two-match series 2-0.