Mahmudullah scored a valiant century but it only delayed the inevitable.
This was South Africa’s fourth win in five matches, while Bangladesh suffered their fourth defeat.
Earlier, Quinton de Kock hit a brilliant 174, his third century of the tournament, as South Africa piled up 382-5.
But left-handed opener De Kock responded with a third hundred in five World Cup innings — after scores of 100 and 109 against Sri Lanka and Australia — as he continued his superb start to what the 30-year-old has said will be his last major one-day tournament.
Heinrich Klaasen followed up with a blistering 90 just days after his 109 in South Africa’s 229-run thrashing of reigning champions England at the Wankhede amid soaring heat and humidity on Saturday.
All of Bangladesh’s seven-stong attack suffered as Bangladesh bowling coach and former South Africa spearhead Allan Donald looked on, none more so than new-ball paceman Mustafizur Rahman whose nine wicketless overs cost 76 runs.
Fit-again Bangladesh captain Shakib Al Hasan, appearing in his fifth World Cup, was not spared either during a return of 1-69 in nine.
South Africa briefly faltered after Bangladesh’s early double strike but De Kock and stand-in captain Aiden Markram (60) then shared a stand of 131.
It was no surprise when Markram, again leading South Africa while regular captain Temba Bavuma remained sidelined by illness, decided to bat first upon winning the toss given the Proteas posted a mammoth 399-7 after being sent in by England.
South Africa were faltering after Reeza Hendricks and Rassie van der Dussen fell in quick succession.
Markram was in fine touch until he tamely chipped Shakib to long-off.
But De Kock completed his 20th hundred in 150 ODIs before, in sight of becoming just the third batsman to score a World Cup double century, he sliced Hasan Mahmud to deep backward point.
He faced 140 balls in total, including 15 fours and seven sixes.
Klaasen ensured there was no respite with eight sixes in his 49-ball innings before he holed out in the last over.
