The competition is split into three pools of four teams - with the winner of each pool guaranteed a semifinal place. The fourth semifinal place is taken by the second-placed team with the highest number of competition points. South Africa are currently ranked second in Pool B with six points and France second in Pool C also with six points.
The Baby Boks have to play the undefeated England in their final pool encounter and France must take on Australia. Even if one of France or Australia do secure a bonus point victory and finish equal with New Zealand on competition points, the defending champions are likely to have a superior points differential to see them through.
Coach Rob Penney said his side were heartbroken at the loss to Wales, but were the architects of their downfall.
Wales had to make three times as many tackles and were constantly under pressure.
The Baby Blacks dominated possession and territory but couldn't convert their pressure into points in difficult wet conditions.
"We are very disappointed with the result, the effort and energy was there but not the accuracy," said Penney. "Our game management was poor and the Welsh made us suffer for that.
"The boys are desperately keen to do well, you will never see a New Zealand team lie down and I didn't feel we were beaten. We were on the scoreboard but we got into positions and it just didn't happen for us.
"The boys are heartbroken at the moment. They must get up, we have another job to do in four or five days [against Fiji] so we look forward to that."
What was hard for New Zealand to accept was that they had defeated Wales 92-0 in last year's competition.
But surprise results have been a theme of this tournament - a competition that has become increasingly important in developing players to graduate into the full test ranks.
Ireland defeated South Africa in the opening game of Pool C and Argentina followed that with a crunching victory against Australia.
The young Pumas beat Australia 15-3 - using their superior physical approach to better handle the difficult conditions.
That victory means Argentina are favourites to progress as they have already beaten France and finish their pool encounter with the bottom-placed Scots.
Australia will meet France and need to win that game and hope Scotland can perform a miracle.
The adverse weather conditions in Stellenbosch have resulted in the field at the Danie Craven Stadium cutting up and the tournament organisers have decided to shift the remainder of the tournament to Newlands in Cape Town.
