Rabada bowled Tamim Iqbal in the third ball of his second over and then had Litton Das and Mahmudullah in the next two deliveries to complete the set, joining Bangladesh's Taijul Islam, who achieved the feat against Zimbabwe at the same ground last December.
The 20-year-old pacer later added three wickets to his tally to finish with 6-16, the best ever haul by a debutant, bettering the record of West Indies' Fidel Edwards, who claimed 6-22 against Zimbabwe in 2003.
The other South African to achieve the feat is Allan Donald who took 5-29 against India at Kolkata in 1991.