Laura Wolvaardt's team will have to hope that England beat West Indies on Tuesday to ensure qualification of the last-four due to the Caribbean women having a better net run-rate.
The Proteas restricted Bangladesh to 106-3 in their 20 overs in Dubai as Marizanne Kapp starred with the ball, taking a wicket and going for just 10 runs from her four overs.
Tazmin Brits (42) and Anneke Bosch (25) led their side to the cusp of victory, leaving Kapp and Chloe Tryon to finish the job and leave last year’s runners-up well placed for another semi-final appearance.
Bangladesh opted to bat but lost their first wicket after just two balls with Dilara Akter caught behind without scoring off the bowling of Kapp.
Shathi Rani and Sobhana Mostary began the recovery with a flurry of boundaries, notably a powerful six from the former but she was dismissed for 19 just two balls later when Bosch pouched a good catch on the slide.
Sobhana and captain Nigar Sultana put on 45 for the fourth wicket, the Tigresses’ best partnership of the tournament, but Sobhana’s defiant knock came to an emphatic end when she was clean bowled for 38 by leading wicket-taker Nonkululeko Mlaba.
Nigar battled bravely to end of the innings, finishing 32 not out and helping her side pick up 23 runs off the final two overs and set the Proteas 107 for victory.
The Proteas Women made a solid start with the bat in reply with a succession of early fours but a welcome wicket arrived for Bangladesh when Laura Wolvaardt (7) was stumped off the bowling of Fahima Khatun.
Just four runs came off the next two overs as Bangladesh threatened to reel South Africa in before a timely boundary arrived from Bosch with the final ball of the sixth over to keep her side ahead of the required run rate.
Bangladesh needed to take their chances but spurned a big one when Brits was dropped in the deep on 21, an error which also yielded a four for the Proteas to add insult to injury.
South Africa were coasting by this stage and Brits and Bosch carved out a 53-run partnership before the latter was caught out trying to finish things off quickly, with Fahima once again responsible for a big scalp.
Brits then followed Bosch back into the hut as Ritu Moni struck to offer Bangladesh some late hope but the foundations for victory had already been laid.
Kapp and Tryon ensured there was no late drama and clinched victory with 16 balls to spare. South Africa will now wait to see how the other results in their group pan out before making plans for the knockout stages.
