South Africa had won 23 of their 24 clashes against Bangladesh in all formats coming into the game but, with Du Plessis the only batsman to make a real impact, the Tigers may have fancied their chances chasing 148 for four.
It was not to be, though, and just three Bangladesh batsmen made double figures as the team recorded just 96.
AB de Villiers was moved up to open by South Africa but he was gone for two off the final ball of the first over.
Arafat Sunny sent one down on a decent length and De Villiers’ attempt flay through the off side only found the hands of Mashrafe Mortaza.
Du Plessis and and Quinton de Kock then each found the boundary, De Kock hitting a six off Nasir Hossain, but he was gone for 12 later in the same over in similar fashion to De Villiers as he found Litton Das.
South Africa then steadied but could not significantly raise the rate and when two wickets fell in three overs, a shock looked like it could be on the cards.
JP Duminy went for 18 off Sunny with Nasir taking a smart catch at deep midwicket and when David Miller (one) was lbw to Shakib Al Hasan, South Africa were 90 for four in the 14th over.
Du Plessis had brought up his 50 off 35 balls between those two wickets and he and Rilee Rossouw (31 not out) guided the Proteas to a seemingly chaseable total.
But Bangaladesh were not up to the task and collapsed inside 18.5 overs.
Both openers were gone within the first two overs as Tamim Iqbal gloved to the wicketkeeper off Kyle Abbott for five and Soumya Sarkar (seven) failed to deal with Kagiso Rabada’s bouncer which found Duminy at deep square-leg.
Mushfiqur Rahim (17) and Shakib got Bangladesh to 50 without further loss but the partnership was ended when the wicketkeeper found Miller off Duminy.
Sabbir Rahman followed for four as De Kock made a smart catch behind off Duminy and five balls later Nasir (one) was gone, finding Rossouw on the drive off Aaron Phangiso.
Any slim chance of victory effectively disappeared when key man Shakib departed for 26 as he found Wayne Parnell off David Wiese and, while Das added 22 on his T20 debut, none of the other Bangladesh players could reach double figures.