Williamson was unbeaten on a career-best 192 while Corey Anderson was 16 not out as New Zealand reached 488-3 at tea on the third day, leading Pakistan's first innings total of 351 by 137 runs.
New Zealand, who trail the three-match series 1-0 after losing the first Test in Abu Dhabi and drawing the second in Dubai, dominated the day through Brendon McCullum's firey 202 and equally dominating batting by Williamson.
A flat Sharjah stadium pitch did not give hapless Pakistani bowlers any hope of a fightback and it was only after they took the second new ball with score at 421-2 that they could dismiss Ross Taylor, caught off leg-spinner Yasir Shah for 50.
Williamson's previous best of 161 not out was against the West Indies at Barbados in June this year.
In the morning McCullum became one of only four batsmen to score three double hundreds in a year.
The New Zealand skipper scored a punishing 188-ball double hundred and created a new second wicket record for New Zealand in all Test cricket with 297.
McCullum jumped out of his crease to hit Shah over the stadium roof at long-on for his 11th six to complete his double hundred off just 186 deliveries.
Michael Clarke (four scores of over 200 in 2012) Ricky Ponting (three in 2003) and Don Bradman (three in 1930) -- all from Australia -- are the only other players to have scored three or more double hundreds in a year.
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