Paul John's men will have to overturn their earlier pool defeat to the Kiwis who ran out 24-7 winners at the So Kon Po Stadium.
New Zealand, along with Fiji and Samoa booked their place in the Cup quarter finals after maintaining their 100% records in the pool stages.
Wales began day two looking to make amends after gifting South Africa victory on day one. Wales began brightly against New Zealand with Richard Smith scoring early to give Alex Walker a simple conversion. The Kiwis hit back just before the halftime hooter through Tim Mikkelson.
But in the second half the Kiwis showed their pedigree and took their chances when they came along. Lolagi Visinia, Kylem O'Donnell and Ardie Savea scored unanswered tries as New Zealand strolled to the top of their pool.
Wales completed their pool fixtures with a stirring 42-7 win over USA which meant they qualified for the Cup knockout stages - albeit a quarter-final clash against firm favourites New Zealand.
Dan Fish and Smith led the rout with a brace of tries apiece with Lee Williams and Craig Price also crossing the white-wash.
Wales captain Richie Pugh was delighted his side had stopped the rot in Hong Kong, gaining confidence from the win against USA.
"The boys put in a professional performance against USA to earn ourselves a Cup quarter-final against New Zealand. New Zealand will be firm favourites but we've shown we can compete with the big boys - we just have to cut out the basic mistakes and take our chances when they come along."