Blackcaps bowlers have run through the Uganda batting order to lay the foundations for a first group victory in a campaign that has already seen them eliminated from the Twenty20 World Cup.
After falling to Afghanistan and West Indies in their opening two matches, New Zealand's fate was sealed, when the hosts easily accounted for Papua New Guinea.
With nothing but pride to play for, the Kiwis barely allowed their rivals into the contest, with veteran bowlers Trent Boult and Tim Southee both flirting with hattricks, as they dismissed the Africans for just 40 runs - one more than the alltime tournament record low.
In reply, New Zealand lost opener Finn Allen in the run chase, but Devon Conway showed some form, hitting four boundaries, including two to complete the task in the sixth over.
The win elevates the Blackcaps from bottom of their group to third, but unable to catch Afghanistan or West Indies, with one fixture remaining against winless PNG.
Boult wasted no time putting Uganda on the ropes, taking wickets with the third and fourth balls of the opening over, before Alpesh Ramjani kept out the hattrick attempt.
Boult and Southee kept the clamps on the top order, reducing them to 2/3 in the fourth over, and only Kenneth Waiswa, with two boundaries, was able to reach double figures.
Wickets continued to fall regularly, with part-time spinner Rachin Ravindra capturing two apiece through the middle, before the newballers returned for their final overs.
Southee had wicketkeeper Fred Achelam and bowler Juma Miyagi trapped in front of the stumps with successive balls, but tailender Cosmas Kyewuta survived another six deliveries, before he fell to Mitch Santner, caught in the slips by Daryl Mitchell.
Allen and Conway didn't set the world on fire in their chase, but they were helped by wayward bowling that served up nine extras, including six wides.
Allen couldn't resist chasing what should have been another wide down legside and was caught behind, much to his surprise and disgust. Conway was out of touch before he broke a finger three months ago and hadn't shown any form at this tournament, but will take some heart from his unbeaten 22 off 15 balls.
"The guys were pretty good," reflected captain Kane Williamson. "There was obviously plenty there in the surface, which made life difficult, and it was nice to do that job in the first half."
Uganda 40 (Waiswa 11; Southee 3/4) Blackcaps 41/1 (Conway 22no; Riazat 1/10)
New Zealand win by nine wickets
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