Making his Test presentation, Bangladesh left-arm pacer Mustafizur Rahman played astoundingly well and caught four wickets for 37 on his Test introduction to give the hosts the high ground.
He was helped by leg-spinner Jubair Hossain who asserted three for 53.
For South Africa, Temba Bavuma top-scored with 54 and his was the last wicket to fall. He was rejected by Mustafizur.
Other primary scorers were Faf de Plessis (48), Senior member Elgar (47) and Stiaan van Zyl (34).
Openers Tamim Iqbal (one not out) and Imrul Kayes (five not out) stayed unbeaten as Bangladesh were 7-0 at stumps.