Saturday's victory in Kolkata was the non-Test side's second win of the tournament after their shock defeat of South Africa.
The Netherlands, as was the case against South Africa, were indebted to wicketkeeper-batsman Edwards, whose innings top-score of 68 led a recovery from 63-4 to 229 all out.
The Tigers, chasing a seemingly modest target of 230, collapsed to 70-6 and were eventually dismissed for 142 as they suffered a fifth defeat in six World Cup games.
Mehidy Hasan Miraz's 35 was the top score against a Netherlands attack missing spinner Roelof van der Merwe through illness.
The Netherlands' win was all the more creditable as it came just days after their World Cup record 309-run defeat by Australia.
Edwards, however, was dropped twice on nought in the same Mustafizur Rahman over, Liton Das flooring him in the gully before wicketkeeper Mushfiqur Rahim grassed a tougher, diving chance.
Netherlands paceman Paul van Meekeren then returned fine figures of 4-23 as the Tigers were bowled out with more than seven overs remaining.
"We thought that if we could get somewhere around 220 plus, we would have a chance," said Edwards.
He added: "We spoke at the start of the tournament about giving ourselves a chance at the semis. That looks tricky, but that'll remain our goal."
'As bad as it gets'
Bangladesh, for all they had plenty of support at Eden Gardens in what is a Bengali-speaking region of India, were "sloppy" in the field according to Tigers captain Shakib Al Hasan and even worse with the bat.
"We have been poor with the bat all tournament and this is as bad as it gets," said star all-rounder Shakib, appearing in his fifth World Cup
Bangladesh lost both their openers on 19.
Edwards held a simple chance after Liton miscued a reverse sweep off spinner Aryan Dutt before taking another catch when Tanzid Hasan edged Logan van Beek.
Van Meekeren then had Shakib, trying to cut a lifting ball that was too close to him caught behind for just five.
The Tigers were all but beaten at 70-6 when Mushfiqur was bowled for one by a fine van Meekeren delivery that jagged back.
Fellow veteran Mahmudullah, fresh from a hundred against South Africa, only managed 20 before he was well caught by Dutt off Bas de Leede.
Van Meekeren ended the match when he had Taskin Ahmed caught in the deep.
Earlier, Edwards shared partnerships of 44 with de Leede and 78 with Sybrand Engelbrecht, who made a useful 35.
The Netherlands were struggling at 4-2 following the loss of openers Vikramkjit Singh and Max O'Dowd after Edwards won the toss.
But Wesley Barresi, in his first match of the tournament, made a run-a-ball 41 before he was caught off a mistimed drive.
Edwards, who made 78 not out against South Africa, then overcame a faltering start to post a 78-ball fifty before he spooned Mustafizur to backward point.
