Bangladesh all-rounder Shakib Al Hasan hit a fighting 68-ball 64 with seven boundaries in his 200th one-day worldwide but no other batsmen cashed in on good starts.
Bangladesh's innings turned on Mushfiqur being run out when the Bengal Tigers were cruising at 2-110 - he and Shakib had been cruising when the keeper was run out for 19. Both the teams are coming from comfortable wins in their previous matches, and would like to wrest momentum in their camp early into the tournament.
With Williamson nowhere in the frame, all Rahim had to do was collect the ball and dislodge the bails.
Tamim Iqbal made ideal at the striker's end that could have hit the stumps directly.
Mashrafe refused to criticise Mushfiqur for his mistake but was left ruing the missed opportunity.
Mehidy struck again five balls later as he took out Tom Latham for a duck.
But when their finishers Colin de Grandhomme (15) and Jimmy Neesham (25) each took a gamble too many, Santner and the tailenders still had 27 to get.
The game took another huge swing with Mosaddek's double strike as he sent back Taylor in the 39th over and Neesham in the 44th. With bowling figures of 9.2-0-47-4, Matt Hardy for the highest wicket-taker for New Zealand.
"It's always valuable when you have a like-for-like bowling to you in the nets", Latham said.
He turned the lifeline into a slow-but-safe 40 in a rejuvenating stand of 105 with Ross Taylor. But the latter ran himself out on 19 looking for a quick single following a bad mix-up in the 24th over.
ICC Cricket World Cup - Bangladesh v New Zealand - The Oval, London, Britain - June 5, 2019.
Apart from Mo. Saifuddin has 29 and Mo. The trustworthy pair of Shakib Al Hasan and Mushifiqur Rehman were asked to rebuild as Williamson was happy to have a slip and a leg-slip in the 18 over.
After putting in to bat first, Bangladesh openers started positively as they added 45 for the first wicket.
For all we know, we might not see another game at this year's World Cup where a sub-250 total produces the excitement to match what we saw between Bangladesh and New Zealand.
Henry exploited the pressure with four wickets, taking his tournament tally to seven, including two in as many balls as he had Mashrafe Mortaza caught at third man and bowled Saifuddin to end the innings.
Meanwhile, Rohit Sharma scored an unbeaten 122 to guide India to a straightforward six-wicket win against South Africa in their opening Cricket World Cup match. Easily the best all-rounder produced by Bangladesh, he was the 4 wicket to fall at 151 in the 31 overs, for Bangladesh's top score of 64 off 68 balls.