Both Australia, bidding for an unprecedented third successive World Cup title, and New Zealand have six points after a pair of Super Eights wins plus the two points they each received for beating their fellow qualifiers during the pool phase.
Australia, who top the standings on run-rate, have looked in ominous form during a run of five wins from five games and have yet to be held to a total under 300 in a match at this tournament.
But in February the Black Caps thrashed Australia 3-0 at home during the Chappell-Hadlee series albeit the visitors were without the rested duo of skipper Ricky Ponting and wicket-keeper Adam Gilchrist while top-order batsman Michael Clarke had a hip injury.
All three are back in the team now with Australia determined to prove that a run of five one-day defeats in a row (England beat them 2-0 in Australia during the finals of the CB Series) was no more than a blip.
New Zealand play Australia in Grenada on April 20 and left-handed opener Fleming, who struck 102 not out against Bangladesh, believes recent experience could work in his side's favour.
"It's going to take a number of things to stop Australia winning the World Cup. It's assessing conditions, then playing as well as you can," he said.
"We've done that in the past, and we're more familiar with them now because we've faced them a lot which helps. We're looking forward to playing them because they are the best."
New Zealand's latest victory was set up by another disciplined all-round bowling performance which saw Bangladesh bundled out for 174.
Jacob Oram led the way with three for 30 while fast bowler Shane Bond turned in another impressive display in taking two for 15 from 10 overs as New Zealand exacted revenge for their surprise two-wicket warm-up loss to Bangladesh.
Fleming and Hamish Marshall (50 not out) then saw them home with an unbroken second-wicket stand of 134 in a win achieved with more than 20 overs to spare.
New Zealand's display in the field was all the more creditable as quicks Michael Mason (calf strain) and James Franklin (migraine) managed just three overs between them before leaving the field.
"It was a great performance with the ball, not a lot in the pitch so to restrict a team to around 170 was where the game was won," said Fleming.
Bond, who has taken eight wickets in four matches at this World Cup at an average of just over 10 apiece, once more looked in fine form and Fleming was as impressed as anyone else.
"The way's he's been doing it is with subtlety, changes of pace, a little reverse swing and the length that he's hitting is top-class."
Fleming's hundred against Bangladesh was only the 34 year-old's eighth in 275 one-day internationals.
But he believes his current form is as good as it has ever been.
"My form in this World Cup has been outstanding, I've just been running myself out. But I'm in some of the best form I've ever had, striking the ball well, and it was nice to push on."
New Zealand, apart from a brief wobble during their opening group victory against England, have yet to be truly tested at this World Cup but Fleming didn't believe his side were at a disadvantage.
"We're doing everything we've had to do but we are looking forward to being put under pressure," said the captain, whose side beat hosts West Indies by seven wickets at the Sir Vivian Richards Stadium here Thursday.
"The Windies was a pressure game and we responded well.
"Three in five days (New Zealand play Ireland in Guyana on April 9, Sri Lanka in Grenada on April 12 and South Africa on April 14) is increbibly tough, but if we keep doing the things we're doing, there's no reason why that won't help us in pressure situations."