South Africa and New Zealand had earlier lost semi-finals to Australia and India respectively.
Batting first after winning the toss, New Zealand were bowled out for just 90 in 36.5 overs. South Africa chased down the target in just 14.4 overs to end at 94 for two.
Earlier, left-arm paceman Jan Frylinck (two for 18 off five overs), playing his second game of the tournament, started off well for South Africa.
Frylinck snapped up New Zealand opener Ben Horne and number three batsman Will Young from successive deliveries, but was denied a hat-trick.
The third-wicket stand of 28 runs between Joe Carter (20) and Robert O'Donnell (13) steadied the ship for New Zealand.
South Africa paceman Calvin Savage (three for 14 off four overs) broke the stubborn partnership, dismissing O'Donnell in the 11th over. Savage's spell helped him earn the Player of the Match award.
Later leg-spinner David Rhoda spun a web around the New Zealand tail, picking up four for 26 off 9.5 overs.
Chasing the paltry target, South Africa were well served by opener and wicket-keeper Quinton de Kock (50, 43b, 9x4) who got the side off to a brisk start.
Left-arm spinner Theo van Woerkom (one for 34 off four overs) and Ish Sodhi (one for 17 off 3.4 overs) were the only wicket-takers for New Zealand.
In the end, South Africa ran home easy winners in just 14.4 overs and sealed the third position in the ICC U19 Cricket World Cup 2012.
Brief Scores:
New Zealand 90 all out in 36.5 overs (Connor Neynens, Joe Carter 20; David Rhoda 4-26, Calvin Savage 3-14)
South Africa 94 for two in 14.4 overs (Quntinon de Kock 50, Theunis de Bruyn 19 not out).
