The All Blacks defeated Australia to climb to the peak of the Championship table, but the Springboks will secure the championship provided that they defeat Argentina in their final game later on Saturday.
Tupaea scored a brace of tries as the All Blacks claimed a extra-point 28-14 victory in a drenched match in Perth to go a four-point margin in front of the Springboks.
Nonetheless, the South African squad will attain successive titles should they defeat the Pumas at Twickenham.
Centre Quinn Tupaea, who stepped in for the excluded Billy Proctor, swung the contest in the All Blacks' advantage with two rapid touchdowns toward the end of the initial period.
Carter went over in the 8th minute to hand the All Blacks an initial advantage, although Australia reacted with three successful penalties from the foot of Edmed.
Tupaea's two tries, in the 30th minute and again in the 36th, provided the New Zealand a 17-9 advantage at the break.
Australia's Len Ikitau got a touchdown for the Australians halfway through the final half, before and after penalties from New Zealand's McKenzie.
However George Bower came off the bench to barge over seconds after the end signal sounded to confirm the win for New Zealand and hand them the bonus point.
Given a four-point allocation for a triumph, and the Springboks possessing a significantly higher points difference than the All Blacks, the Springboks simply must defeat the Pumas to take the title.
They thumped Argentina 67 to 30 in the earlier match last Saturday, and due to the short break in matches, the Argentinian team have chosen to play their home game in London.