After limiting Bangladesh to just 106-3 in 20 overs, South Africa reached their target with 16 balls to spare.
With three wins and one defeat, they sit top of Group B with six points.
However, 2009 champions England, with two wins so far and with two games still to play, are likely to secure one of the semi-final spots.
That would leave South Africa and West Indies vying for the last place.
West Indies, the 2016 champions, have four points but a better net run-rate than South Africa although the Caribbean side have to face England in their concluding pool game on Tuesday.
Player of the match Tazmin Brits steered 2023 runners-up South Africa to victory on Saturday with a steady 42 off 41 balls, an innings which featured five fours.
Anneke Bosch made a run-a-ball 25 before Marizanne Kapp (13 not out) and Chloe Tryon (14 not out) saw their side home.
"The way we started with the ball was amazing. Would have loved to chase it down faster and that was a message that went out, but we didn't get there," said South Africa captain Laura Wolvaardt who bemoaned her side conceding 13 extras when Bangladesh batted.
Bangladesh had won the toss and chose to bat but lost opener Dilara Akter off the second ball for nought.
The Asian side struggled to make any headway against the South African attack.
Sobhana Mostary top-scored but her 38 took 43 balls with skipper Nigar Sultana making an undefeated 32 from 38 deliveries.
Kapp claimed 1-10 from her four overs of medium pace while Nonkululeko Mlaba finished with 1-11.
Off-break bowler Mlaba has enjoyed an impressive tournament with the ball and has nine wickets from four games, making her the leading wicket-taker.
"There's a lot of intent and emotion there," said Bangladesh captain Sultana after a tournament which brought them just one victory -- an opening day win against Scotland.
"In this kind of tournament you have to be mentally strong. A lot of people came to support us, and it felt like we were at home. Although we couldn't do well, there was unconditional love."
