The New Zealand skipper also underscored his ranking as the world’s premier batsman
At stumps, the tourists were already in trouble at one down for eight, with Kyle Jamieson adding to his five-wicket haul in the first innings by removing Shan Masood for a duck.
Should New Zealand win the Test it will confirm their ranking as the number one side in the world for the first time – to go with Williamson’s promotion as the number one batsman – and keep alive their chance of making the World Test Championship final.
It was a relentless performance from Williamson who became only the second New Zealander after Brendon McCullum to score four double centuries.
He should have been out for 177 on the first ball after the first of two rain stoppages, but as has happened several times in the Test the chance was put down.
The day resumed with New Zealand 286/3, 11 runs in arrears and with conditions favourable for the bowlers who had cloud cover and a ball only five overs old.
But for every plan Pakistan set to dismiss Williamson, he had an answer – with a range of strokes from silky touches to powerful drives.
Along the way he followed Ross Taylor and Stephen Fleming to become only the third New Zealander to pass 7,000 runs.