The Proteas had come up well short against hosts England in Thursday's opener and a failure to ever really get to grips with the Bangladesh batsmen, playing their first match, cost them here.
Bangladesh's ODI record and the biggest total of the tournament so far - 330-6 - saw Shakib Al Hasan (75) and Mushfiqur Rahim (78) combine for a 142-run third-wicket stand that gave South Africa a mountain to climb.
An opening partnership of 60 was belatedly broken by Andile Phehlukwayo with his second ball to Tamim Iqbal (16), yet there was no slowing the Tigers.