Miller hammered the fastest century in T20 internationals - he reached 100 off 35 balls to smash the record by 10 balls - to propel South Africa to 4-224 batting first.
Bangladesh was 141 all out in 18.3 overs, another heavy defeat on a difficult five-week tour for the visiting team.
It was the first time that South Africa had won every game in three series against a touring team, Cricket South Africa said.
While South Africa gained valuable preparation under new coach Ottis Gibson ahead of tours by India and Australia, Bangladesh failed to live up to the promise it showed recently in home series.
South Africa took the test series 2-0, winning those matches by 333 runs and then an innings and 254 runs. It swept the ODIs 3-0, with winning margins of 10 wickets, 104 runs and 200 runs.
Bangladesh came closest to something to celebrate when it went down by 20 runs in the first T20.
In the final game of the tour, Miller hit five sixes in a row in the 19th over, and nine sixes and seven fours in all in his record-breaking innings.
He beat the record of fellow South African Richard Levi, who scored a century off 45 balls against New Zealand in 2012.
“Obviously a really special feeling.” Miller said.
“Don’t quite know what went on there but I was just trying to watch the ball and back myself.”
Miller’s five sixes off the first five balls of the 19th over from Mohammad Saifuddin helped him move from 57 to 88 in the space of an over.
He just missed out on becoming only the third batsman to hit six sixes in an over in international cricket when he could only drive the final ball from Saifuddin through the covers for one.
The only players to hit six sixes in an over in an international are South Africa’s Herschelle Gibbs and India’s Yuvraj Singh.
Bangladesh was left to seriously rue that it dropped Miller when he was yet to score, although it was a tough chance that wicketkeeper Mustafizur Rahim put down after a full-length dive.
South Africa’s total was the joint 13th highest in T20 internationals with Miller’s century and opener Hashim Amla hitting 85 off 51 balls.
Before Miller arrived South Africa was only 3-78.
“Last 10 overs I thought we were going to restrict them,” Bangladesh’s Al Hasan said, “but Miller came in and credit to him ... he had all the answers.”
Needing more than 11 an over from the start, Bangladesh didn’t have the firepower to threaten the Proteas, a story that played out through most of the tour.
Soumya Sarkar made 44 but South Africa was always in control, with stand-in captain JP Duminy and fellow spinner Aaron Phangiso taking two wickets each.