Chasing a revised 170-run victory target under the Duckworth-Lewis method, openers Soumya Sarkar (90) and Tamim Iqbal (61 not out) showed little respect for the South African bowlers as the hosts romped home with nearly 14 overs to spare.
Bangladesh's third successive home ODI series victory this year underlines their growing stature in 50-over cricket and proves their recent series wins against Pakistan and India were no fluke.
Batting first, South Africa could never recover from a top-order collapse and posted a below-par 168-9 in a conTest that was reduced to 40-overs-a-side following a lengthy rain interruption.
David Miller (44) and JP Duminy (51) tried to bring some respectability to the tourists' total after Shakib Al Hasan (3-33) had wrecked the South African top order.
"It's a huge moment for Bangladesh cricket," Tamim said in a pitchside interview.
"Beating South Africa was no easy task but hats off to the boys for playing amazingly," the opener said after his team's memorable win.
Having levelled the series with Sunday's emphatic seven-wicket win in Dhaka, the hosts looked determined to pull off another upset as they reduced South Africa to 50 for four in the 16th over.
Heavy rain forced the players off the field and when play resumed after more than two hours, Miller and Duminy tried to rebuild the innings but it was not enough in the end.
"Very disappointing indeed, I think we misread the conditions," South Africa captain Hashim Amla, who was left to rue his decision to bat first, said after the embarrassing loss.
"We showed that we are rusty and we have not played good cricket over the last two games. Bangladesh are the in-form team and they showed why," said the right-hander who fell for 15, becoming Shakib's 200th ODI victim.
Sarkar, whose belligerent 75-ball knock included 13 boundaries and a six, was named player of the match and the series.
The teams remain in Chittagong for the two-Test series starting on Tuesday.
Scorecard
South Africa Innings
Q. de Kock b M. Rahman 7
H. Amla c Rahim b Al Hasan 15
F. du Plessis c Rahim b Al Hasan 6
R. Rossouw c Rahim b Mahmudullah 17
D. Miller c Sa. Rahman b Mortaza 44
J. Duminy c Das b R. Hossain 51
F. Behardien c Sa. Rahman b Al Hasan 12
K. Rabada b M. Rahman 1
K. Abbott b R. Hossain 5
M. Morkel not out 1
Extras (lb-3 nb-2 w-4) 9
Total (for 9 wickets, 40 overs) 168
Fall of wickets: 1-8, 2-19, 3-45, 4-50, 5-113, 6-149, 7-155, 8-167, 9-168 J. Duminy
Bowling
M. Rahman 8 - 0 - 24 - 2
M. Mortaza 5 - 0 - 29 - 1
S. Al Hasan 8 - 0 - 33 - 3
R. Hossain 6 - 0 - 29 - 2(nb-2 w-2)
Nas. Hossain 8 - 0 - 30 - 0
Mahmudullah 5 - 0 - 20 - 1
Bangladesh Innings
T. Iqbal not out 61
S. Sarkar c Amla b Tahir 90
L. Das not out 5
Extras (lb-5 w-9) 14
Total (for 1 wickets, 26.1 overs) 170
Fall of wickets: 1-154
Bowling
K. Abbott 5 - 0 - 27 - 0
K. Rabada 6 - 0 - 41 - 0(w-3)
M. Morkel 5 - 0 - 36 - 0(w-1)
I. Tahir 6.1 - 1 - 37 - 1(w-2)
J. Duminy 4 - 0 - 24 - 0(w-3)
Image: Soumya Sarkar
Photograph: Quinn Rooney/Getty Images