The last of those wins came in 1953, when a Bleddyn Williams-captained side beat the New Zealanders 13-8 in front of 56,000, their largest-ever win over the Kiwis.
Since then, it has been a 64-year winless drought as Wales search on for their fourth test victory against the three-time world champions. The All Blacks, on the other hand, have enjoyed a 29-match winning streak against the seventh-ranked team in the world.
The winning run has thrown up many classic encounters between both teams. In 1978, locks Andy Haden and Frank Oliver milked a last minute penalty by diving from a lineout, which allowed Brian McKechnie to slot the penalty, handing the All Blacks a controversial 13-12 win in Cardiff.
The 1987 World Cup semi-final in Brisbane was the setting that Welsh lock Huw Richards was sent off after getting knocked out by Buck Shelford for punching his All Blacks teammate Gary Whetton.
Shelford received no penalty, but Richards became the first player in the tournament's history to be sent from the field. The All Blacks went on to thrash their opponents 49-6.
Other notable tests include their high-scoring 2003 World Cup clash, with the Steve Hansen-coached Wales side fighting hard but eventually succumbing to a 53-37 defeat in Sydney.
Their 2006 and 2008 meetings are also memorable due to controversies surrounding the haka. In the first of those two meetings, the All Blacks chose to perform the pre-match ritual in their changing room against their non-playing teammates as a result of a disagreement with the Welsh Rugby Union about the haka being performed prior to the Welsh national anthem.
Two years later, the haka was met with a two minute-long stare off by Warren Gatland's team, as both sides refused to look away from each other as they were cheered on by an electric crowd at Millennium Stadium.
This week's clash is noteworthy thanks to the well-documented personal rivalry between the two coaches, with Hansen and Gatland set to square off for the first time since Gatland led the British and Irish Lions to a series draw in New Zealand four months ago.
Should the 54-year-old Wales coach steer his side to a win on Sunday morning, he would earn bragging rights over his compatriot for what would have to be considered a highly successful year against Kiwi opposition.
However, despite their thrilling yet not-overly-convincing win over Scotland last week, a victory to Hansen's men seems to be a much more realistic proposition, especially considering Wales' dire 13-6 win over Georgia seven days ago. The All Blacks to extend their unbeaten run against Wales to 30 straight tests is a result that should be expected.
Line Ups:
Three changes have been made to the All Blacks' starting line up from the team that ran out against Scotland in Edinburgh last week.
Perhaps the most significant change comes at No. 8, with captain and 109-test veteran Kieran Read ruled out of the year ending clash due to a back injury. His replacement is one-test rookie Luke Whitelock, who captained the side in their mid-week match against the French XV in Lyon last week.
The news is significant for Whitelock's older and vastly more experienced brother Sam, who will skipper the team for the very first time. His locking partner will be Patrick Tuipulotu, who comes into the starting side at the expense of Luke Romano who has a foot injury.
Vaea Fifita also drops out of the match day squad, with Liam Squire promoted from the bench to starting blindside flanker. Rieko Ioane, who was supposedly ruled out for the remainder of the year due to shoulder damage, has remarkably recovered in time to retain his place on the left wing.
Only one change has been made on the bench, with Scott Barrett filling the vacant number 19 jersey left by Squire.
On the other hand, Wales have made sweeping changes throughout their side in the wake of their ugly win over Georgia last week.
Just three players have retained their places in the Welsh starting side, with halfback Rhys Webb and centre Scott Williams staying in the number 9 and 13 jerseys, while Hallam Amos switches wings to start at number 14.
Many familiar names from the Lions tour have also been listed to start, including Ken Owens, Alun Wyn Jones, Taulupe Faletau, Dan Biggar and Leigh Halfpenny. Loose forward Justin Tipuric, who played in five matches on that tour, has been named on the bench.
Despite having such talent at their disposal for this weekend's test, Gatland's men are tasked with taking down the All Blacks without many key figures. Ross Moriarty (back), Sam Warburton (neck), Jonathan Davies (foot), George North (knee), and Liam Williams (abdomen) have all been ruled out with injury, robbing the Welsh of five Lions players and 287 caps worth of international experience.
All Blacks: 15. Damian McKenzie, 14. Waisake Naholo, 13. Ryan Crotty, 12. Sonny Bill Williams, 11. Rieko Ioane, 10. Beauden Barrett, 9. Aaron Smith, 8. Luke Whitelock, 7. Sam Cane, 6. Liam Squire, 5. Sam Whitelock (c), 4. Patrick Tuipulotu, 3. Nepo Laulala, 2. Dane Coles, 1. Kane Hames.
Reserves: 16. Codie Taylor, 17. Wyatt Crockett, 18. Ofa Tu'ungafasi, 19. Scott Barrett, 20. Matt Todd, 21. TJ Perenara, 22. Lima Sopoaga, 23. Anton Lienert-Brown.
Wales: 15. Leigh Halfpenny, 14. Hallam Amos, 13. Scott Williams, 12. Owen Williams, 11. Steff Evans, 10. Dan Biggar, 9. Rhys Webb, 8. Taulupe Faletau, 7. Josh Navidi, 6. Aaron Shingler, 5. Alun Wyn Jones (c), 4. Jake Ball, 3. Tomas Francis, 2. Ken Owens, 1. Rob Evans.
Reserves: 16. Kristian Dacey, 17. Wyn Jones, 18. Leon Brown, 19. Cory Hill, 20. Justin Tipuric, 21. Gareth Davies, 22. Rhys Priestland, 23. Jamie Roberts.
Odds:
The All Blacks are strong favourites to defeat the Welsh for the 30th consecutive test, with the TAB paying $1.11 for a New Zealand victory. Comparatively, Wales are paying $6.10.
As per usual, the two wingers are the joint favourites to score the first try of the match, with World Rugby Player of the Year nominee Rieko Ioane and Waisake Naholo, who has been impressive on this tour, both paying $6.50.
It would be an understatement to say that the TAB aren't overly confident Wales will score the first try, with the Welsh favourite to score first being Steff Evans. He is paying a whopping $21 to dot down first, the same amount the betting agency is paying for Luke Whitelock.
How to watch:
The Herald will be live blogging the game, and Radio Sport will have live commentary. Sky TV will be showing the match live on Sky Sport 1 at 6.15am.
