Jakob Bhula was the first New Zealand wicket to fall for 44, with Rachin Ravindra continuing his side's momentum before being dismissed for 76.
Dale Phillips (43) Max Chu (35) and Finn Allen all made solid contributions as New Zealand posted their opponents a substantial target after reaching 279/8 in their allotted overs.
The Kiwi bowlers roared into action to take the first South African wicket with the fourth ball of the reply.
The arrival South African number four batsman Hermann Rolfes anchored a fight-back, as he went on the attack, smacking 108 runs before being removed.
A 106-run partnership with Jean du Plessis had their side back in the match.
When Du Plessis went for 54 the New Zealand side held the ascendancy, with South Africa 199 for the loss of seven wickets.
The New Zealand bowlers then wrapped up the tail to dismiss South Africa for 208, to finish with an impressive 71-run victory and a Group A unbeaten record.
Man of the match Rachin Ravindra took four wickets for 32 runs to back up his batting heroics, with Jakob Bhula and Mathew Fisher finishing with two wickets apiece.
On Friday India finished their preliminary assignments in the cup, posting a third emphatic victory by defeating Zimbabwe by 10 wickets.
Zimbabwe won the toss and made a brave decision to bat first against the tournament front-runners. At five down for 110 runs, Zimbabwe were fighting for survival - finally being removed for 154 with 11 balls remaining in their innings.
Anukul Roy finished his three appearances at the Bay Oval with a 10-wicket haul, after taking four wickets for 20 runs.
Included in his four-wicket bag were the Zimbabwe key wickets of Milton Shumba and Liam Roche, who were both looking to have settled in before Roy weaved some magic with the ball.
India strolled to the top spot in Group B when they cruised home in the 21st over without losing a wicket.
Man of the match Shubman Gill led the way with a dashing 90 runs off just 59 balls, which included thirteen fours and shot over the boundary fence.
Gill received plenty of quality support from Harvik Desai who hammered a half-century.
India will now meet Bangladesh in a Super League quarterfinal next Friday (26 January 2018) in Queenstown.
ICC Under 19 Cricket World Cup at Bay Oval, Mount Maunganui
19 January
Zimbabwe 154 (M Shumba 36, LN Roche 31, W Madhevere 30; AS Roy 4/20, A Singh 2/10, A Sharma 2/22) lost to India 155/0 (S Gill 90, HM Desai 56)
20 January
New Zealand 279/8 (R Ravindra 76, JJNP Bhula 44, DN Phillips 43, MW Chu 35, FH Allen 27; K Molefe 2/49) defeated South Africa 208 (H Rolfes 108; JF de Plessis 54; R Ravindra 4/32, JJNP Bhula 2/25, MJ Fisher 2/36)
