The test match moved Kane into number-one position on the International Cricket Council world rankings following the match-winning century. He also broke Brendon McCullum's record for most test runs by a New Zealander in a calendar year.
The near single-handed New Zealand victory helps cap off a golden 2015 for the former Tauranga Boys' College student. Earlier this month he won the coveted Bayleys Real Estate Sportsman of the Year award at the Bay of Plenty Sports Awards after breaking several records.
"He's had a fantastic year, whichever way you look at it. We are very proud," Mr Williamson said.
"We are excited about the achievement but we know that cricket can lift you up and pull you down. It's quite a tough game at times."
Mr Williamson coached Kane in cricket through until he was 12 or 13 years old "then of course he showed some promise and with Kane I thought, 'I just want to be a parent'".
He then enlisted the training skills of Dave Johnston.
Mr Williamson said as proud as he was of his boy, he never held the lofty dreams that his son would one day reign as world champ, which he he now does.
"We never really think like that. All we knew is that from a very early age, naturally he showed some ability and scored a lot of runs. But cricket ... because it can pull you down very quickly, it can be a real rollercoaster. We try not to get ahead of ourselves and I think you see that in Kane - that calmness, even if he's thrilled about what he's done and what he's achieved.
"People close to him understand the work that goes in," he said.
Mr Williamson said Kane got a lot of satisfaction when the team did well, more so than himself individually.
"He's so team driven. He's never focused on personal gain, he just tries to get a bit better. When he practises, he practises with a purpose. It's never for the sake of practising.
"There's always something in mind."
Mr Williamson said Kane would have been happy enough with reaching his century "but number one is pretty outstanding no matter how you look at it".
Mr Williamson looked forward to catching up with Kane ahead of Christmas, after which he was due to travel to Christchurch to play Sri Lanka at the ANZ International Series on Boxing Day.