Williamson raised his 11th Test century with 10 runs off a Mitchell Johnson over nearing lunch as the Black Caps defied Australian attempts to close out their first innings.
At lunch, New Zealand were 273 for seven with Williamson unconquered on 112 and Doug Bracewell not out 16 to trail Australia's 556 for four declared by 283 runs.
It was another fine batting achievement by the well-credentialed Williamson, who has also scored centuries against Sri Lanka, Pakistan, West Indies, England, India, Bangladesh and South Africa in his five years of playing Test cricket.
Williamson played a lone hand on the third morning after the Black Caps lost the wickets of BJ Watling and Mark Craig, while Bracewell was dropped on four by Adam Voges at slip off Johnson.
Wicketkeeper Watling added 67 runs for the sixth wicket with Williamson before he fell to the first ball of Johnson's opening over of the day.
He dabbled outside the off-stump and edged to Peter Nevill for 32 off 59 balls to leave the Kiwis at 185 for six.
The first objective for the Black Caps was avoiding the follow on and they still need a further 84 runs to make Australia bat again.
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