Scott Styris earlier returned impressive bowling figures of 4 for 43 runs and was ably assisted by Jacob Oram who took three wickets and Shane Bond with two.
New Zealand quickly lost opener Peter Fulton, who continued up the order up in the absence of the injured Lou Vincent, when he was caught by Tamim Iqbal off Syed Russel for 15.
Bangldesh made a solid start with an opening stand of 55 but although every one of the top order made it past 20 no-one was able to go on and make a big score.
However, tailender Mohammad Rafique struck two sixes in an unbeaten knock of 30 and put on 34 for the tenth wicket with Rasel to at least give his side a total they could possibly defend
It was to be Bangladesh's only success in the field as Fleming went on to make his eighth one-day century.
The only dark cloud on the Kiwis’ horizon were injuries to seam bowlers Michael Mason and Craig McMillan.
The Black Caps, who have already lost strike bowler Daryl Tuffey and opening batsman Lou Vincent to injury during the course of the tournament, saw Mason and then McMillan bowl just nine balls each before they were forced to leave the field at the Sir Vivian Richards Stadium.