The All Blacks created the benchmark between 1965 and 1969 and repeated the feat between 2013 and 2014 while South Africa won 17 consecutive internationals from 1997 until 1998.
The streak has given New Zealand the 2016 Rugby championship title - their fourth since the Tri Nations series involving New Zealand, Australia and South Africa was revamped in 2012 to allow Argentina into the competition for southern hemisphere teams.
Ian Foster, the All Blacks assistant coach, said the desire to create history was one of the factors driving a team that last suffered defeat in August 2015, losing 27-19 to Australia in Sydney.
"Chasing records is interesting," he said. "It is about challenging ourselves to be the best we can."
New Zealand have changed four of the side that began the 36-17 triumph over Argentina.
Jerome Kaino, who has recovered from injury and Matt Todd replace Ardie Savea and Liam Squire as flankers, while lock Sam Whitelock returns in place of Patrick Tuipulotu.
The other change is on the left wing with Waisake Naholo, who pulled a hamstring in the opening round win over Australia, recalled in place of Julian Savea.
"We have been able to bring fresh players back into the group, which is vital at this time of the year and allows us to continue to grow some depth," explained head coach Steve Hansen.
While New Zealand hunt a collective prize, Bryan Habana, a winger nearing the end of a glittering career and 25-year-old Beauden Barrett, a rising fly-half star, are targeting individual records.
Habana, 33, South Africa's leading tries scorer needs four more touchdowns to overtake the 69-try Test record of Daisuke Ohata.
Barrett has notched up 65 points during the 2016 tournament and requires 24 more to surpass the 88 points scored by South Africa's Morne Steyn in 2013.
South Africa go into the clash in second have made two changes to the side that beat Australia in Pretoria on 1 October.
Centre Damian de Allende and scrum-half Faf de Klerk, dropped due to poor form, have been given further chances because Jesse Kriel and Rudy Paige are sidelined through injury/
"The All Blacks will be a huge test," said South Africa head coach Allister Coetzee. "They are the number one side in the world and are showing great form at the moment."