Miller, courtesy nine sixes and seven fours, scored 101 runs off 36 balls, reaching his ton on the 35th ball.
In the process, South Africa scored 224-4 at the end of their 20 overs to set a 225-run target for Bangladesh.
Earlier, Levi scored the fastest ton off 45 balls against New Zealand at Hamilton.
South African AB de Villiers and Indian Lokesh Rahul share the third spot with 46-ball tons.
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