Joe Rokocoko scored again to make him the highest try scorer in the tournament with eight.
Australia beat Samoa to take the Plate final, whilst France defeated Canada to take the Bowl.
In the Shield final, Georgia were rewarded for their impressive showing in this tournament with a 20-14 win over Scotland. Georgia had accounted for Ireland in the semi-final.
Final Cup: New Zealand 54 South Africa 14
Final Plate: Australia 45 Samoa 14
Final Bowl: France 22 Canada 19
Final Shield: Georgia 20 Scotland 14