The New Zealand captain finished on 200 not out as his side posted a record score of 715 for six declared in their first innings - a lead of 481 runs - midway through the afternoon session at Seddon Park.
Bangladesh were 174-4 at the close of play, still 307 runs adrift from making New Zealand bat again and staring at a massive innings defeat.
Soumya Sarkar was 39 not out with stand-in captain Mahmudullah on 15 at the close of play.
New Zealand's previous highest innings total of 690 was scored against Pakistan in Sharjah in 2014.
The hosts had resumed on Saturday on 451-4 with Williamson on 93 and nightwatchman Neil Wagner one not out.
Wagner smashed a quickfire 47 from 35 balls, falling short of his maiden test half century, before BJ Watling was dismissed for 31 in the final over before lunch to set up a Colin de Grandhomme cameo after the break.
The aggressive all-rounder hit 76 not out, which included five sixes and four boundaries, as he and Williamson added 110 runs in 91 balls.
Williamson, whose highest test score is 242 not out, brought up his second double century when he dispatched a short delivery from Abu Jayed behind square for his 19th boundary.
He then had a short chat with de Grandhomme and declared the innings closed, giving his bowlers about 45 minutes to bowl at Bangladesh before the tea break.
Tamim Iqbal and Shadman Islam gave the visitors a rollicking start with an opening partnership of 88 before Shadman fell to Wagner's short-pitched delivery for 37.
Trent Boult then dismissed Mominul Haque (eight) and Mohammad Mithun (nought) in successive overs to leave Bangladesh at 110 for three.
Tamim added to his impressive attacking 126 in the first innings with 74 in the second but was bounced out by Tim Southee and his dismissal left Bangladesh reeling on 126-4.
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
