Published: 2017-10-29 22:34:34 BdST
Miller, who was dropped on zero, reached his ton off 35 balls, beating the previous best mark of 45 deliveries set by compatriot Richard Levi against New Zealand in 2012.
South Africa managed 224 for four off their 20 overs, with Miller not out 101 from 36 balls as he crashed seven fours and nine sixes.
Bangladesh were in trouble early in their reply and never recovered as they were bowled out for 141 in 18.3 overs.
Five of Miller's sixes came in one over off Bangladesh seamer Mohammad Saifuddin as he showed remarkable timing in smashing the ball to all parts of the ground.
"It's a really special feeling," Miller told SuperSport. "I tried to watch the ball and back myself. I was scratchy to be honest in the beginning and towards the back end it turned out to be sweet."
South Africa won all seven tour matches against Bangladesh across the three formats, which included two tests, three One-Day Internationals and two Twenty20 Internationals.