Edwards leads from front as Netherlands held to 229 by Bangladesh
Several Bangladesh bowlers took two wickets apiece at Eden Gardens, with the Netherlands in trouble at 63-4 and 107-5 after Edwards won the toss.
But Edwards shared partnerships of 44 with Bas de Leede (17) and 78 with Sybrand Engelbrecht as the Netherlands batted out their 50 overs.
Edwards won the toss and batted as the Netherlands looked to recover from a World Cup record 309-run defeat by Australia.
But Vikramjit Singh chipped the fit-again Taskin Ahmed after making just three to Shakib Al Hasan and fellow opener Max O'Dowd then fell for a duck when he edged Shoriful Islam to slip to leave the Netherlands 4-2 in the third over.
Wesley Barresi, 39, in his first match of the tournament, repaired some of the damage with a run-a-ball 41 before he was caught off a mistimed drive.
And 63-3 became 63-4 in the 15th over when Colin Ackermann (15) top-edged a sweep off Mustafizur Rahman to short fine leg.
De Leede kept the Tigers at bay before he was caught behind off an excellent delivery from paceman Taskin (2-43), fit following a shoulder injury, to leave the Netherlands 107-5.
But Edwards, whose unbeaten 78 propelled the Netherlands to a shock win over South Africa earlier in the tournament, was still there.
Tonga-born and Australia raised, but Dutch qualified through his grandmother, the 27-year-old Edwards held firm to complete a 78-ball fifty with just three fours.
He was eventually out when he spooned a catch off Mustafizur to backward point, with Engelbrecht lbw to Mahedi Hasan soon afterwards as the innings fell away.
Both teams have identical records of one win and four defeats from their opening five World Cup matches.
Brief scores: Netherlands 229 in 50 overs (S Edwards 68) v Bangladesh