The men will close out their first day of competition against South Africa at 10:53 a.m. ET.
But as the game neared it send Blitzboks replacement Tim Agaba showed tremendous strength to power over the tryling and seal the match and tournament for South Africa.
Chasing their first tournament win since Vancouver in 2016, the New Zealanders clawed their way back with tries to Scott Curry and Andrew Knewstubb after Specman was yellow-carded for a deliberate knock on.
Kwagga Smith piled more misery on Kenya with a seventh try for the Blitzboks before Rosco Speckman came off the bench to complete the rout with a converted effort and secure South Africa a Main Cup quarter-finals ticket with a game to spare.
"As a first tournament for us this season I'm really proud of the continuous effort and the attitude the boys displayed in every single game", he said.
"We deliberately didn't put the guys into anything like this in pre-season as it's such a long season for us so it was always going to be a little bit of a risk".
They faced the challenge of New Zealand, who followed a 14-12 quarter-final win over Kenya by then overcoming England 14-5 in the last four.
"We want to focus on our processes and it we leave the result and result doesn't go our way then we're still happy".
Tom Bowen scored two tries and Tom Mitchell and Ruaridh McConnochie also crossed as England won 28-21.
This was just after speedster Collins Injera had scored a brace of tries to inspire the national sevens team to a 29-15 victory over Canada in their opening match.