Sarfaraz Khan and Washington Sundar pulled India out of trouble with a 110-run stand for the fifth wicket.
Nepal, which won the qualifying event in Malaysia last year to return to the World Cup after missing the previous tournament in 2014, bowled out the Kiwis, which was chasing 239 for victory, for 206.
While captain Raju Rijal top-scored for Nepal with 48, seamer Dipender Airee’s three wickets and off-spinner Prem Tamang’s two helped clinch the dramatic win.
Dale Phillips scored 41 to make a late victory bid for New Zealand before he was last out to spark joyous celebrations in the Nepalese camp.
“This was a great win for us,” said Rijal. “We fielded brilliantly to effect three run outs and that turned the match for us.”
New Zealand skipper Josh Finnie said his side messed up what should have been a comfortable run-chase.
“We made the target more difficult for ourselves,” he said. “We must now win the next two games against India and Ireland if we are to progress.”
Three-time champion India overcame a shaky start against Ireland to open its campaign with a 79-run victory in Mirpur in another Group D match, which was produced by ICC TV and aired around the world by 15 broadcasters.
India was reduced to 55 for four after being sent in to bat, before Sarfaraz Khan and Washington Sundar pulled their team out of trouble with a 110-run stand for the fifth wicket.
Sarfaraz smashed 74 off 70 balls with included seven boundaries, while left-handed Sundar hit a polished 62.
Irish seamers Rory Anders and Joshua Little picked up three wickets each, but tail-ender Zeeshan Ansari boosted India’s total with a run-a-ball 36 at the end.
Ireland was bowled out for 189 in reply as Rahul Batham took three for 15 and Avesh Khan finished with two for 24.
Sarfaraz said he was not satisfied despite winning the man of the match award.
“I should have scored more because I had settled in well,” he said. “Hopefully, I will do better in the remaining matches. But it is good to start the tournament with a win.”
India captain Ishan Kishan was relieved that his side collected maximum points. “We lost some early wickets but runs were done by Sarfaraz and Washington who had an excellent partnership. The fielding effort was great as we inflicted two run-outs at the start and then, the bowlers hit the right areas,” the opener said.
Kishan continued: “I am not that much happy with the batting as we lost early wickets but this was the first match and I am sure we’ll learn from this match and do better in upcoming matches.
“India has won the event thrice, so the expectation level is pretty high. We have to play professionally and try to live up to the expectations.”
Ireland captain Jack Tector chose to look at the defeat positively. “We started the game very well with the ball and then also had a few partnerships which bodes well for the future.”
In Group B games played in Sylhet, Pakistan crushed Afghanistan by six wickets and Sri Lanka overpowered Canada by 196 runs.
Pakistan’s leg-spinner Shadab Khan grabbed four for nine in five overs and seamer Hasan Mohsin took three for 24 as Afghanistan was bundled out for 126 after being sent in to bat.
Tariq Stanikzai scored a fine 53, but eight batsmen failed to reach double-figures against the sustained pressure applied by the Pakistanis.
Pakistan surpassed the modest target in the 32nd over with Zeeshan Malik making 29, Hasan Mohsin an unbeaten 28 and Mohammad Umar 25.
Shadab, playing his first U19 World Cup, admitted he was nervous at the start but settled down to return with excellent figures.
“I tried to bowl as straight as possible without trying too many things,” he said. “I am happy with my performance but more importantly we achieved a convincing win. It has given us tremendous confidence and lifted the entire side.”
Sri Lanka showed why it is one of the tournament favourites when it rattled up 315 for six after electing to bat against Canada.
Skipper Charith Asalanka led the way with 76 off 69 balls, the in-form Shammu Ashan hit 74 off 61 balls, Kaveen Bandara made 61 and wicket-keeper Vishad de Silva scored 51.
Canada was shot out for 119 in reply with Arslan Khan playing a lone hand with an unbeaten 42. Lahiru Kumara, Thilan Nimesh and Damitha Silva claimed two wickets each.
The 11th edition of the biennial 16-nation tournament features nine Test-playing nations and seven Associate and Affiliate Members – Afghanistan, Canada, Fiji, Namibia, Nepal, Ireland and Scotland.
Teams have been divided into four groups with the top two in each advancing to the Super League quarter-finals and the other two qualifying for the Plate championships.
Scores in brief:
Group B - Pakistan beat Afghanistan by six wickets in Sylhet
Afghanistan 126 all out, 41.2 overs (Tariq Stanikzai 53; Shadab Khan 4-9, Hasan Mohsin 3-24)
Pakistan 129-4, 31.3 overs (Zeeshan Malik 29, Hasan Mohsin 28 not out, Mohammad Umar 25; Zia-ur-Rehman 2-31)
Group B - Sri Lanka beat Canada by 196 runs in Sylhet
Sri Lanka 315-6, 50 overs (Charith Asalanka 76, Shammu Ashan 74, Kaveen Bandara 61, Vishad de Silva 51; Abdul Haseeb 2-65)
Canada 119 all out, 39.2 overs (Arslan Khan 42 not out; Lahiru Kumara 2-22, Thilan Nimesh 2-19, Damitha Silva 2-16)
Group D - India beat Ireland by 79 runs in Mirpur
India 268-9, 50 overs (Sarfaraz Khan 74, Washington Sundar 62, Zeeshan Ansari 36; Rory Anders 3-35, Joshua Little 3-52)
Ireland 189 all out, 49.1 overs (Lorcan Tucker 57, William McClintock 58; Avesh Khan 2-24, Rahul Batham 3-15)
Group D - Nepal beat New Zealand by 32 runs in Fatullah
Nepal 238-7, 50 overs (Raju Rijal 48, Sandeep Sunar 39, Aarif Sheikh 39, Kushal Bhurtel 35 not out; Nathan Smith 3-58)
New Zealand 206 all out, 47.1 overs (Glenn Phillips 52, Josh Finnie 37, Dale Phillips 41; Dipendra Airee 3-24, Prem Tamang 2-38)
Group A – Namibia v Scotland, SKICS, Cox’s Bazar
Group C – England v West Indies, ZACS, Chittagong
Group C – Fiji v Zimbabwe, MA Aziz, Chittagong
· Top two sides from each group will progress to the Super League stage while the bottom two sides will feature in the Plate Championship