The Welsh tackling was poor in the first-half and all three tries, from centre Jackson Willison, full back Trent Renata and wing Zach Guildford, could have been stopped.
Yet having shipped that try hat-trick in 21 minutes, the Welsh defence stood firm for the next 48 minutes before replacement centre Winston Stanley cut through for a fourth try with the last play of the game.
"We are very disappointed at the result and we simply didn't stay with them in the first-half," admitted Wales wing Leigh Halfpenny.
"But there was much more hunger in the second half and we came out all guns blazing and made a good job of containing them. We looked pretty good in patches."
Ospreys wing Halfpenny took his tournament tally through the 50 points barrier as he kicked four penalties. Three of them came in the first half as Wales closed the 20 point gap to 14 at the break, 23-9.
New Zealand full back Trent Renata, who ended the game with 21 points, swapped penalties with Halfpenny at the start of the second half and Wales were able to exert some real pressure.
Halfpenny missed with a penalty that would have cut the gap to 11 points and the All Blacks were happy to see Renata slot over his fourth penalty after 58 minutes to leave Wales needing to score three times to win.
Wales coach Justin Burnell's decision to change his half-backs and centre pairing shortly after the third New Zealand try made a huge difference to his side's defensive attitude and the grey shirted Welshmen earned huge praise for their second half display.
New Zealand, winners of the IRB title in 1999, 2001, 2002 and 2004 as well as being last year's runners-up, will now meet South Africa in Saturday's final. The junior Springboks beat defending champions Australia 32-18.
Wales Under 19: Daniel Evans (Llanelli / Scarlets); Jimmy Norris (Bedwas / Dragons), Luke Ford (Wanderers / Blues), Rhys Williams (UWIC/ Scarlets), Leigh Halfpenny (Neath / Ospreys); Gareth Owen (Maesteg / Ospreys), Gareth Williams (Wanderers / Blues); Ryan Bevington (Bridgend / Ospreys), Huw Dowden (Beddau / Blues), Lloyd Elliott (Ospreys), Haydn Pugh (Llangennech / Scarlets), Josh Turnbull (Llanelli / Scarlets), Jevon Groves (Cardiff /Blues), Nicholas Cudd (Tumble / Scarlets), Sam Warburton (capt, Wanderers / Blues).
Replacements used: Tom Williams (Bridgend / Ospreys) for Ford 23; Rhys Webb (Bridgend / Ospreys) for Gareth Williams 25; David Langdon (Ebbw Vale / Dragons) for Owen 25; James Egan (Cardiff / Blues) for Langdon 29; Lloyd Phillips (Narberth / Scarlets) for Groves 35; Ben Roberts (Ebbw Vale / Dragons) for Dowden 35; Sam Hobbs (Pontypridd /Blues) for Elliott 54.