Cape Town - South Africa ended Pool B in second place after losing 24-19 to New Zealand in their final group match on Saturday.
The Blitzbokke's chances of beating New Zealand were dealt a blow as they ended the first half 12-0 down.
A valiant comeback by South Africa fell short as the Kiwis did enough to hold on to victory.
South Africa will now face a quarter-final showdown against Fiji on Sunday.
Tries: Dippenaar, Senatla, Speckman
Conversions: Speckman x 2
Tries: Curry, Curtis, Mikkelson, Stowers
Conversions: Kaka, Webber