A sluggish batting display saw the Tigresses post just 117 for 5, a target South Africa chased down with four balls to spare.
Needing a win to keep their hopes alive, Bangladesh endured the worst possible start as Marizanne Kapp bowled Juairiya Ferdous with the very first ball of the innings.
Fellow opener Taj Nehar also failed to make an impact, scoring just one run before departing.
With both openers back in the pavilion early, Sobhana Mostary and Sharmin Akhter attempted to rebuild the innings but struggled to accelerate.
Sharmin scored 22 off 29 balls, while Mostary top-scored with a patient 42 from 48 deliveries before both fell trying to increase the scoring rate.
Captain Nigar Sultana Joty provided late momentum with a brisk 32 off just 20 balls, helping Bangladesh cross the 100-run mark and finish on 117 for 5 in their allotted 20 overs.
Bangladesh made the perfect start with the ball as Marufa Akter dismissed South Africa captain Laura Wolvaardt with the first delivery of the chase.
However, Tazmin Brits and Annerie Dercksen steadied the innings with a crucial partnership. Brits scored 20 off 24 balls, while Dercksen anchored the chase with 45 from 45 deliveries.
Left-arm spinner Nahida Akter removed both set batters to revive Bangladesh's hopes briefly. Late wickets of Marizanne Kapp (16 off 21) and Nadine de Klerk (15 off 14) kept the contest alive, but Chloe Tryon finished the job with an unbeaten 8 off 5 balls as South Africa reached the target in 19.2 overs.
Bangladesh finished their World Cup campaign with two wins from five matches, defeating only the Netherlands and Pakistan to end fourth in Group 1.
