New Zealand led 14-7 at halftime and successfully stopped the Blitzboks of scoring opportunities by slowing the pace of the game and controlling ball possession and territory.
Rosko Specman and Justin Geduld were the South African try scorers, while Sam Dickson, Kurt Baker and Lewis Ormond scored for the Kiwis.
South Africans were considered the favourites to win the first Canadian event after they had beaten Wales and Fiji by convincing margins earlier in the day.
They crushed Wales 31-0 in the quarterfinals and then defeated the powerful Fijians 31-19 in their semi-final encounter.
Fiji lead the way with 106 points despite their shock 19-12 loss to Australia in the playoff match for third place.
They are closely followed by South Africa (105) and New Zealand (104).
Coach Neil Powell said he was proud of the Blitzboks’ effort over the two days.