The All Blacks have now won 13 tests in a row, a streak which started with their 41-13 victory over Australia at Eden Park last year, their final match before the World Cup.
The record test streak for top tier nations is 17, which the All Blacks have accomplished twice - in 1965-69, and more recently in 2013-14. The Springboks also accomplished it between 1997-98.
In 2014, Australia stopped the All Blacks' winning streak in Sydney with a 12-all draw.
Should the All Blacks win their next four tests against the Pumas and Springboks, whom they play twice each, home and away, the record-breaking 18th victory could be achieved against Australia at Eden Park on October 22, the Bledisloe Cup dead rubber.
It's a big 'if', and the record will be the last thing occupying the minds of the All Blacks, who will be looking to make incremental improvements before their next test against Argentina at Waikato Stadium a week on Saturday. But it's there all the same, and this All Blacks team under Steve Hansen, the first to win back-to-back World Cups, has shown a willingness to embrace challenges.
The last time the All Blacks were on the brink of equalling the record, hooker Keven Mealamu said: "It will be something we walk towards and really embrace because it hasn't been done before and it would be awesome to be the team to do it."
Argentina, who moved ahead of France to seventh on World Rugby's rankings following their 26-24 victory over South Africa in Salta at the weekend, will be buoyed by their success after pushing the Boks close a week earlier in Nelspruit. But they have never beaten the All Blacks, and have injury concerns over first-five Nicolas Sanchez, lock Tomas Lavanini and key midfield back Juan Martin Hernandez.
The Springboks, who lost a test to Ireland in June, have struggled to get their attack going against the Pumas in the first two tests of the Rugby Championship as they adapt to life under new coach Allister Coetzee. Coeztee, the former Stormers coach who took over from Heyneke Meyer following the World Cup, has been criticised at home for his team's performances and apparent lack of a game plan.
Following the Australia test at Eden Park in October, the All Blacks will play Ireland twice - once in Chicago and once in Dublin - plus Italy and France on their November tour this year.
In October 2012, the Wallabies stopped the All Blacks' winning streak at 16 with an 18-all draw in Brisbane.
All Blacks next fixtures:
Sept 10 v Argentina in Hamilton
Sept 17 v South Africa in Christchurch
Oct 2 v Argentina in Buenos Aires
Oct 9 v South Africa in Durban
Oct 22 v Australia in Auckland
World Rugby rankings
1. New Zealand 96.30 points
2. England 89.49
3. South Africa 85.08
4. Australia 84.23
5. Wales 82.49
6. Ireland 81.67
7. Argentina 81.44
8. France 80.75