Scott Styris (4-43) and Jacob Oram (3-30) set the Black Caps on their way with a fine effort in the field.
Only Mohammad Rafique (30no) offered any resistance as Bangladesh were bowled out for a miserly 174.
And Fleming (102no) and Hamish Marshall (50no) shared a 134-stand to ease the Kiwis home with 20.4 overs to spare.
The only drawback for the Kiwis in a dominant display was that their injury problems continued to mount, with Michael Mason limping off the field in just the third over with a calf strain.
James Franklin also sat out most of the innings with a migraine, but it mattered little as the Black Caps rattled through the Tigers line-up.
Going into the game with a 100% record, New Zealand were in confident mood and captain Stephen Fleming had no hesitation in putting Bangladesh into bat after winning the toss.
However, clearly stung by criticism from their coach that they had been giving their wickets away too casually, Bangladesh's openers dug in.
With the ball swinging and seaming a touch early on, Bangladesh set their stall out not to lose wickets and it resulted in a terribly pedestrian run rate.
Four maidens in the first 10 overs highlighted the Tigers' unwillingness to open their shoulders during the early powerplays, and only Iqbal seemed happy to play the occasional aggressive shot.
The pair did bring up an opening half-century stand, though, and it appeared Bangladesh might be on the verge of building a decent total.
But Oram had other ideas, and having accounted for Iqbal thanks to a brilliant stumping from Brendon McCullum, he had Omar edge behind in his next over.
That brought Aftab Ahmed and Saqib Al Hasan together, and Ahmed was obviously keen to up the run-rate, crashing three boundaries in his 27, including a splendid cut through the off-side for the shot of the day.
However, his aggressive intent caused his downfall when he lofted Styris down substitute fielder Mark Gillespie's throat at long-on and Oram (3-30) followed up a superb bowling spell with a fine throw from the outfield to run out skipper Habibal Bashar (9).
Suddenly, Bangladesh were wobbling and two overs later Shane Bond (2-15) returned to the attack to bowl Hasan (25) and Mushfiqur Rahim (0) in the same over to leave the Tigers in disarray.
Next it was Styris' turn to notch a few quick wickets with some splendid wicket-to-wicket bowling to continue what had been a sensational tournament from the all-rounder so far.
Mohammad Ashraful and Mashrafe Mortaza both played round deliveries and Gillespie took his second high catch of the innings to account for Abdur Razzak.
Six wickets had fallen in under nine overs for just 18 runs and the Kiwis were on the brink.
Rafique hit two glorious sixes over deep midwicket during a late cameo that took Bangladesh past 150 in a last-wicket stand of 34, but it never looked enough.
Fleming had been struggling for runs in this tournament, and the Kiwis skipper's fine innings was not chanceless here.
Twice the 34-year-old survived when leading edges fell safe early in his innings, and the Kiwis' running between the wickets again left a lot to be desired at times.
However, with such a small target to chase, New Zealand could afford the odd risk and Fleming and Fulton put on a steady 44 for the first wicket to lay the foundations for an easy win.
Syed Rasel ended their stand when Fulton toed an attempted drive up into the air and straight to Tamim Iqbal at mid-on.
That brought Marshall to the crease and it was the number three that was fortunate to survive some poor running.
Aftab Ahmed needed to only pick and throw down the stumps from close in to run him out early in his innings, but the Bangladesh fielder missed the ball, while Saqib Al Hasan dropped a difficult chance at mid-on in the 19th over.
Fleming and Marshall soon settled in, though, and following a quiet middle 10 overs, the pair opened up late on to accelerate their innings perfectly.
The New Zealand skipper in particular took a shine to the spinners and struck three huge sixes to ensure he reached his ninth one-day century in style.
With 10 other boundaries to his name, his 92-ball knock was a welcome return to form the day after his birthday.
But arguably even more welcome was Marshall's knock - a late-comer into the squad as an injury replacement.
The batsman brought up his 50 with the final ball of the innings, smashing Mohammad Ashraful for six, for the ideal end to a ruthless New Zealand victory.
It puts the Black Caps on the verge of qualifying for the semi-finals.
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