New Zealand's tactic of targeting the back of the lineout paid off, and they used the long pass to good effect to stymie that rush defence.
Their skills were evident through most of the encounter, though the sting had long since gone from the game after that devastating opening salvo.
Centre Sio Tomkinson applied the finishing touches with a 95m intercept. Man of the match went to lock Quinten Strange, who scored a try, from a Malo Tuitama chargedown, and galloped around the field with a high work-rate, as well as discharging his core roles.
New Zealand now have 26 tries from four games in the tournament.
Coach Scott Robertson was happy that the sun finally came out, and even happier with the performance.
"It showed we can play some really good rugby. I'm stoked for the young men. We came out wanting to make a statement (at this tournament) and play our style. We hadn't had the chance to do that until today," said the new Crusaders coach.
New Zealand will now face Australia, who lowered them on the Gold Coast last month, to decide fifth position after they beat Scotland 35-19, gaining revenge for their pool defeat to the home nation.
The final will, for the first time, be contested between two-time champion England, who have bounced back from a poor Six Nations campaign, and Ireland, who lowered New Zealand last week. England defeated South Africa 39-17 and Ireland put 37-7 on Argentina in the semifinals.
Other results saw France win 41-27 over Japan and Georgia edge Italy 18-17.
The finals will be on Sunday morning (NZT). New Zealand will play Australia at 1.30am, with the final set to go for 6am.
New Zealand 71 (Caleb Makene 3, Shaun Stevenson 2, Jonah Lowe, Hamish Dalzell, Hapakuki Moala-Liava'a, Leni Apisai, Quinten Strange, Sio Tomkinson tries; Jordie Barrett 7 con, Stevenson con) Wales 12 (Joe Gage, Harrison Keddie tries; Jarrod Evans con)
HT: 35-5