His unbeaten 200 in the first test has him on the cusp of becoming the format's best batsman again.
The New Zealand skipper has lifted his ranking points to 915, just seven shy of India's Virat Kohli.
Williamson's rating points are the highest by any New Zealander in test cricket with Richard Hadlee the only other player from his country to cross the 900-point mark with a best of 909 points in bowling.
Williamson could surpass Kohli with strong performances in the remaining two tests.
He was No1 briefly in 2015.
Black Caps openers Tom Latham and Jeet Raval have also made good progress after their centuries in Hamilton. Latham's score of 161 has lifted him one place to a career-best 11th position and just three points shy of South Africa's Faf du Plessis, who is in 10th place with 702 points. Raval's maiden century, after seven fifties, has helped him gain five slots and reach 33rd position.
Men's test rankings:
1 - Virat Kohli (India) - 922
2 - Kane Williamson (NZ) - 915
3 - Cheteshwar Pujara (India) - 881
4 - Steve Smith (Australia) - 857
5 - Joe Root (England) 763
