Ayabonga Khaka took 4-32, including her 100th wicket in one-day internationals, as South Africa cruised to victory on Saturday after they posted 207 from 49.5 overs.
Bangladesh, who won the toss and bowled first, were dismissed for 175 in the final over of their innings.
Opener Laura Wolvardt anchored South Africa's innings with 41 from 52 balls in challenging batting conditions.
Bangladesh used their slow medium and spin bowlers to good effect on a slowish pitch at the University Oval, making stroke play and placement difficult.
Captain Sane Luus batted 50 minutes for 25 before being run out when South Africa were 5-119 in the 34th over, needing to lift the run rate.
Marizanne Kapp and Chloe Tryon took on the role of accelerating the scoring and combined in a partnership of 71 for the sixth wicket.
Kapp made 42 from 45 balls and Tryon 39 from 40.
Bangladesh made a strong start to their chase with Shamima Sultana (27) and Sharmin Akhter (34) sharing a 69-run opening stand in 19.3 overs.
However, their departures within three runs of each other were the catalyst for a regular loss of wickets.
Captain Nigar Sultana made 29 and Ritu Moni 27 as they gave themselves a chance at 7-170 with four overs left.
But Khaka helped suppress the Bangladesh chase.
"We are proud of Ayabonga Khaka, she is our golden arm at the moment," Luus said.
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