South Africa declared their first innings at a daunting 575-6 thanks to Tony de Zorzi's 177 and Wiaan Mulder's unbeaten 105, before the tourists reduced Bangladesh to 38-4 on day two of their second Test on Wednesday.
Mominul Haque was batting on six with Najmul Hossain Shanto unbeaten on four with Bangladesh trailing by 537 runs when poor light brought play to a close early.
Mulder endured nervy moments and dived into the crease to avoid being run out before his first century in Tests, but he got there in the next over with a big six down the ground off spinner Taijul Islam and raised his arms aloft.
With De Zorzi and Tristan Stubbs also getting their maiden centuries, it marked only the second time in Test history that three batsmen had done so in the same innings.
Gerry Gomez, Robert Christiani and Clyde Walcott were the first trio, when the West Indies faced India in 1948.
After South Africa's stand-in captain Aiden Markram called time on their innings, Kagiso Rabada gave them the ideal start by removing Shadman Islam for a duck and Zakir Hasan for two before Mahmudul Hasan Joy fell to Dane Paterson for 10.
Nightwatchman Hasan Mahmud was castled by Keshav Maharaj for three, leaving Bangladesh in deep trouble.
Earlier, De Zorzi picked up from where he left off after notching up his century on Tuesday, as South Africa accumulated runs with ease having resumed at 307-2 on a batting-friendly track at the Zahur Ahmed Chowdhury Stadium.
He reached his 150 with a lofted boundary off Taijul and followed it up with another immediately, as the hosts came under pressure early on another hot, humid day on the southeastern coast of Bangladesh.
Bedingham was equally aggressive at the other end and hit a quick-fire 59 but was bowled out by Taijul, who then trapped De Zorzi lbw and removed Kyle Verreynne for a duck shortly before lunch to claim his 14th five-wicket haul.
It was expensive, however, as he finished with 5-198.
Senuran Muthusamy made an unbeaten 68 as he combined well with Mulder in another 100-run stand in the afternoon session and help the Proteas go past 500 runs in Tests for the first time since 2020.
South Africa are 1-0 up in the two-match series after their seven-wicket victory in Dhaka.
