However it could be shortlived if Wales don't beat England at Twickenham on Monday morning (NZT) in the first of two tests dubbed as 'warm-ups' ahead of the World Cup.
Wales will officially be ranked top on Tuesday (NZT) if they win.
South Africa were the last side to be ranked above the All Blacks as number one in the world, in November 2009, with New Zealand since winning the 2011 and 2015 World Cups.
Warren Gatland's side are currently boast a 14-match winning sequence, including a rare win against Australia in November, 2019.
This includes a third Grand Slam since the New Zealander took charge of Wales ahead of the 2008 Six Nations.
The last of those triumphs came as Wales won the 2019 with victory over Ireland in Cardiff in March.
Wales officially being ranked number one in the world would be the first time since the system was introduced in 2003.
Following the 16-16 draw to South Africa in Wellington, the All Blacks held a 1.58 point lead in the rankings over Wales. But last night's loss in Perth saw the All Blacks drop by 1.66 points and into second spot, according to Wales Online.
Last month Hansen said the rankings mean nothing ahead of a World Cup.
"World ranking is an outcome of what you do so it has nothing to do with the World Cup because you don't win the World Cup if you're the number one team," Hansen following his side's tight win over Argentina.
He says they've shown that many times, particularly in 2007 when they were entered number one and exited in the quarter-finals.
The All Blacks have been on top spot for almost a decade. They moved to number one on November 16, 2009, taking the spot from the Springboks after South Africa beat New Zealand three straight times earlier that season.
The rugby ranking system was brought in by World Rugby just before the 2003 World Cup. Since then the All Blacks have held the top spot for more than 13 years.
In a column for the NZ Herald on August 7 (before All Blacks loss), here's what Chris Rattue said:
The world rugby rankings have always been a crock of you-know-what. World rugby is a rort which conspires against Pacific Island nations.
Tonga, Samoa and Fiji are shut out of decision making, battle to keep players and play most major games away from home.
Changes to the top of the world rugby rankings are like bankers swapping seats in first class. Get past the favoured few and it's deck chairs on the Titanic time.
The Pacific Island countries never cop an even break when the major competition structure decisions are made.
World rugby is an old boys club, designed to stay that way.
As the Nations Cup concept collapse showed, old rivalries and self-interest among the Six Nations still shape the game. Visionaries don't have a chance, because Scotland has got the hump with England.
The old guard might not always get along, but better the devil you share a cigar and brandy with than let a threatening newcomer in.
British rugby columnist Stephen Jones, a controversial character in this part of the world, wrote a brilliant column on the subject in June.
The problems aren't just in the north. New Zealand rugby's attitude towards the PI countries has long been a disgrace.
There isn't a clear top team right now but the Welsh climb tears away the rankings facade.
They have put a long winning run together, but all their major victories have been in Cardiff.
Their win against South Africa in Washington DC a year ago was condemned as a farce between two substandard selections.
The last time Wales played significant tests at away venues was in early 2018, when they lost to Ireland and England.
Send Wales on a tour against full strength and well prepared Fiji, Tonga and Samoa teams, and see where their world ranking ends up.
The world rugby rankings represent a sport mistreating its own. The Pacific Island countries are regarded as talent factories and under-prepared cannon fodder for warm up matches.
The powerbrokers pat them on the head, hope they provide some World Cup charm, and make sure they go away before the trophies are handed out.
"Absolute power corrupts absolutely'. The rugby rankings are a reminder of that.