In Mirpur, four of Bangladesh’s top six batsmen failed to reach double digits, with opener Mahmudul Hasan Joy scoring the most runs with 30.
After skipper Najmul Hossain Shanto won the throw and decided to bat on a vivacious pitch, Bangladesh tumbled to 60-6 at lunch and were excused in the subsequent meeting.
Rabada, Wiaan Mulder, a fellow seamer, and Keshav Maharaj, a left-arm spinner, each took three wickets for South Africa.
Mulder eliminated Shadman Islam for a duck when he edged to skipper Aiden Markram at slip with his fourth ball.
Mominul Haque, who was on four when Mulder bowled him, was caught by wicketkeeper Kyle Verreynne with an inswinger, leaving Bangladesh at 13-2.
Najmul had made only seven when he turned into Mulder’s third casualty, chipping to mid-off where Maharaj took the catch.
Bangladesh were wavering at 21-3, which became 40-4 when Mushfiqur Rahim on 11 was bowled by Rabada among bat and cushion as the South African commended arriving at the 300-wicket milestone.
He dealt with the accomplishment in 11,817 balls, the quickest ever, beating Waqar Younis (12,602).
Rabada before long made it 301 Test wickets, eliminating Litton Das for one, with Tristan Stubbs taking a dazzling discover jumping to one side in the gorge.
Maharaj held Mehidy Hasan Miraz in a lbw trap for 13 rounds.
After lunch, Bangladesh lost two additional speedy wickets, with Dane Piedt eliminating Mahmudul and Maharaj catching debutant Jaker Ali, before Rabada and Maharaj finished the tail.
Since the autocratic premier Sheikh Hasina was overthrown in August by a student-led revolution, Bangladesh has not hosted an international cricket match.
Bangladesh are feeling the loss of all-rounder Shakib Al Hasan after security fears constrained him to drop intends to get back.
Last month, Shakib said he would retire from international cricket, but he said he wanted to play one last red-ball series in his home country.
The 37-year-old was likewise a previous legislator in the public authority expelled by the transformation, making him an objective of public outrage.
A day after Shakib fans and those protesting the player near the venue clashed, there was a lot of security around the stadium.