South Africa's win on Saturday means they finish with six points from three wins and a loss in group B.
England, who have two games left in the group stages, and West Indies, who have one more match, are both on four points, with only two teams to qualify.
Opening batter Tazmin Brits top-scored with 42 off 41 balls as South Africa cruised to 3-107 with 16 balls to spare in their comprehensive win.
Bangladesh spinner Fahima Khatun (2-19) had skipper Laura Wolvaardt (7) stumped in the third over but Brits was well supported by Anneke Bosch, who scored a run-a-ball 25 as they put on a key second-wicket partnership of 53.
Earlier, Marizanne Kapp (1-10) and the tournament's leading wicket-taker Nonkululeko Mlaba(1-11) set up South Africa's victory by restricting Bangladesh, who won the toss, to 3-106 on the slow surface of Dubai International Stadium.
Bangladesh batters couldn't score freely against fast bowlers Kapp and Ayabonga Khaka and were restricted to 1-21 in the first six overs.
Sobhana Mostary (38) and captain Nigar Sultana (32no) tried to push the scoring rate along, but South African bowlers always looked in control later in the innings. Mostary hit four boundaries before she was bowled by Mlaba in the 18th over.
Bangladesh, who beat first-timers Scotland in the opening match of the tournament, lost three matches in a row and bowed out of the event with two points.
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