The New Zealanders were eliminated from the earlier tri-series in Australia after qualification for the final had seemed a formality and Fleming, in particular, was the target for some harsh criticism.
But with Shane Bond restored to his destructive best, they handed Australia their first 10 wicket defeat ever in a one-day international this month then successfully chased two daunting targets to record a 3-0 victory.
Victory over a half-strength side suffering from a surfeit of one-day cricket at the end of a crowded season is not in itself a matter for unrestrained celebration.
The series did, though, show that Bond is peaking at the right time, gave further evidence that Ross Taylor is a genuinely exciting batting talent and confirmed that Craig McMillan can still strike the ball with brutal force.
In a cricket world championship run along the lines of the Hong Kong rugby sevens, New Zealand would be serious contenders.
Unfortunately for the Kiwis they seldom field a test or one-day XI with more than half a dozen players of genuine international class and their performances suffer accordingly.
New Zealand have habitually compensated for their deficiencies by fielding a succession of determined, canny cricketers who maximise their talents and never give up, no matter how hopeless the cause may appear to be.
They were among the pioneers in one-day cricket, entering and winning an Australia state competition in the early 1970s at a time when the Australians did not regard them as suitable opponents in test matches.
A decade later they were invited to take part in the annual triangular tournaments in Australia which helped turn a useful team into a force in world cricket.
New Zealand teams usually perform the basics well; bowling straight, fielding competently and accumulating runs down the order.
Bond holds key: In the Caribbean much will depend on the fitness and form of Bond, who rattled the Australians with six for 22 in South Africa at the last tournament and completed another five-wicket haul in the first match of the last series.
New Zealand's other match winner is the giant left-hander Jacob Oram, who struck the fastest one-day century by a New Zealander against Australia, a mark subsequently broken by McMillan.
Oram will miss the opening World Cup game against England after fracturing a finger in the first match against Australia.
Brendon McCullum, who struck 86 not out in the final match against Australia, has become a force in one-day cricket and his lively wicketkeeping has become increasingly impressive.
Left-arm orthodox spinner Daniel Vettori has become New Zealand's key bowler in one-day cricket, a player of high intelligence who varies his flight, spin and angle of delivery.
Otherwise the attack consists of the promising off-spinner Jeetan Patel, who may have a leading role on the slow Caribbean tracks, and the usual clutch of medium-pacers.
Fleming carries a heavy load at opener as, in comparison to Australia and the Asian teams, New Zealand lack real class in the middle order.
Four semi-final spots in eight tournaments testify to New Zealand's ability in one-day cricket. Whether they go further this time depends on the ability of Bond, Oram and McMillan to lift their team a stage higher than their customary competence.
Key Players: Stephen Fleming, Lou Vincent, McCullum, Shane Bond, Vettori.
Squad: Stephen Fleming (capt), Shane Bond, James Franklin, Peter Fulton, Mark Gillespie, Brendon McCullum (wk), Craig McMillan, Michael Mason, Jacob Oram, Jeetan Patel, Scott Styris, Ross Taylor, Daryl Tuffey, Daniel Vettori and Lou Vincent. John Bracewell (coach).
New Zealand Factfile:
World Cup record: 1975 - semi-finalists; 1979 - semi-finalists; 1983 - first round; 1987 - first round; 1992 - semi-finalists; 1996 - quarter-finalists; 1999 - semi-finalists;2003 - super six.
Overall playing record: Played: 517, Won: 219, Lost: 270, Tied: 4, No result: 24.
Highest innings total: 397-5 v Zimbabwe, Bulawayo, 2005.
Lowest innings total: 64 v Pakistan, Sharjah, 1986.
Highest individual score: Lou Vincent (172).
Leading run-scorer: Stephen Fleming (7,654).
Best bowling: Shane Bond (6 for 19) v India, 2005.
Leading wicket-taker: Chris Harris (203).
Highest partnership: Stephen Fleming and Lou Vincent (201, Ist wicket) v Zimbabwe, Bulawayo, 2005.
Most catches (fieldsman): Stephen Fleming (130).
Most dismissals (wk): Adam Parore (141).