When play was called off at 3.54pm, Williamson was unbeaten on 104 and Taylor 105 not out, with the duo adding an unbroken 213 for the third wicket partnership - a record against England.
The England pacer drew Williamson into a poor shot.
Camera IconThe unlucky bowler, Jofra Archer, was in absolute disbelief after Joe Denly put Kane Williamson down.
When Ben Stokes took an around-the-wicket path to New Zealand's key batsman in the fourth over of the final day, it prompted the skipper to glove a short one through to stand-in wicketkeeper Pope.
With Williamson mis-timing the ball gently in the air, it was the simplest of chances for Denly.
"A lot of hard work had to go into saving the match when time didn't allow us an opportunity to win it", he said.
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England's Joe Denly drops a sitter.
The ball was at a knee height and looked so easy that Archer started celebrating it even before the ball reached Denly's hand. Archer, on the other hand, had wheeled away in celebration before Williamson gestured for him to look back.
Williamson, resuming on 96 after the interval, might have been run out when chasing a risky second only for Sam Curran to miss with his shy at the stumps, before sweeping a four to fine leg off Joe Root's bowling made it Test century No 21.
Ross Taylor in action against England.
As the second Test in Hamilton headed towards a mundane draw, Joe Denly inadvertently produced a moment that will live long in the memory - albeit one he would like to forget!
The Black Caps now head to Australia for a three Test series, starting on December 12 in Perth, also playing the traditional Boxing Day Test in Melbourne, and the new year Test in Sydney.
The hosts hold a 110-run lead and barring an almighty collapse and a quick run chase, or a courageous declaration and a batting capitulation, the series will go to New Zealand following their innings win in the first Test.