South Africa openers Dean Elgar (113) and Aiden Markram (143) took the chance, making a 100-plus partnership for the second straight game.
South Africa's batsmen were in rampaging mood on Friday as Bangladesh failed to come up with a plan to either take wickets on check runs on Day 1. However, the 334 runs Bangladesh need to make the home side bat again seems too far fetched a hope. Bangladesh had won the toss and elected to field.
Amla (132) and Du Plessis (135 not out) became the third and fourth centurions of the innings.
Rabada was the most successful bowler with five wickets, while Olivier took three, and Parnell and Keshav Maharaj claimed one wicket each.
Bangladesh ended day two on 7/0 and will continue batting on Sunday at 10:00 local time or 08:00 local time.
Du Plessis followed before lunch, also reaching his century with a four as the boundaries continued to flow for South Africa. He made nearly half the Bangladesh total (70 off 77 balls, 13 fours) before becoming Rabada's fourth victim.
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This was a key race in the Xfinity Series playoff, with the field being cut down from 12 to eight at the end of the night. I remember Watkins Glen earlier this year when we got wrecked ... and we had to come from the back.
Du Plessis and wicketkeeper Quinton de Kock kept the scoreboard ticking with a quickfire 38-run stand before South Africa declared on 573/4.
The only previous occasion on which South Africa scored four centuries in an innings was against the West Indies in a high-scoring draw in St John's in 2004-05.
Soumya Sarkar never looked at ease since walking out in the morning and was undone by yet another unnecessary poke at a ball in the channel outside his off-stump as Faf du Plessis pouched the edge safely in front of first slip.
Mushfiqur was 11 not out when he ducked into a short delivery from Duanne Olivier in the 13th over of the day.
Rabada took over from that point as he sent Imrul Kayes packing for 26 before slicing through the lower order easily.