New Zealand inflicted South Africa's heaviest home defeat as they equalled their own record of 17 straight Test wins with a 57-15 rout in Durban.
The All Blacks ran in nine tries with TJ Perenara, in for Aaron Smith after he was dropped for meeting a woman in a toilet cubicle, scoring twice.
New Zealand's victory completes a clean sweep in the Rugby Championship.
The world champions will set a new Test record for successive wins if they beat Australia in Auckland on 22 October.
New Zealand's current run began in the wake of a 27-19 loss to the Wallabies in Sydney in August 2015.
But few will bet on their trans-Tasman rivals denying them a piece of history given the All Blacks' imperious form when they meet in the third and final Bledisloe Cup match of the season in a fortnight.
The visitors led by a slender 12-9 at the interval, with fly-half Beauden Barrett struggling to find his kicking range and his team-mates having been uncharacteristically wasteful after creating openings.
But Steven Hansen's men roared clear in the second half with Barrett and winger Israel Dagg joining Perenara in crossing twice.
Wallabies beat Pumas
Australia beat Argentina 33-21 at Twickenham to condemn the Pumas to bottom spot in the final standings.
Wallabies centre Samu Kerevi scored twice to help his side to victory in the first Rugby Championship match to be staged in the northern hemisphere.
Number eight Leroy Houston, who is back at former club Bath from Queensland Reds until the end of October as injury cover, made his Test debut for Australia off the bench at the age of 29.
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