Starc bowls fastest Test delivery
Taylor finished day three at the WACA unbeaten on 235, having shared in a third-wicket partnership of 265 with Williamson (166), as New Zealand reached stumps on 510 for six.
But Warner could not find the same form, and was out for 25th just half an hour into the day. Guptill was dismissed for 1 by pacer Mitchell Starc early in the innings, while Latham was caught off spinner Nathan Lyon’s bowling by a waiting Steven Smith at first slip.
Usman Khawaja will miss Australia’s next two Tests because of a hamstring injury, opening the door for Shaun Marsh, Cameron Bancroft or Michael Klinger to earn a call-up.
Williamson boosted his own growing stature as one of the best batsmen in the world with a second century in the series, his fourth in nine innings this year.
After narrowly surviving a decision review on 78, he reached triple figures with his 12th boundary, having faced 118 balls.
The others in the select group are South Africa´s Alan Melville and Hashim Amla, West Indian Everton Weekes and Pakistan´s Shoaib Mohammad.
Williamson struck 24 boundaries off 250 balls for his second century of the series, after scoring 140 in the 208-run defeat in the first test at the Gabba last week.
In a truncated morning session ” 17 minutes lost to a troubled sight screen behind the bowler’s arm ” New Zealand scored over a run a minute.
It was the more pedestrian pace of Josh Hazlewood that broke the third-wicket partnership when Williamson toe-ended an attempted pull to Mitchell Johnson at mid-on, while Mitchell Marsh’s 130-kph effort clean bowled McCullum for 27. The milestone made him the first Kiwi to score a Test double century against Australia and he now holds the record for the highest score by a visiting player at the Waca Ground in Test cricket.
The new Burswood stadium now being constructed on the other side of the Swan River, in full view of the WACA, is being tipped to open with an Ashes Test between Australia and England in 2017-18.
Burns made 40 before chopping a ball on from the bowling of recalled seamer Matt Henry (1-51).
Taylor had emerged from a form slump and was 165 not out, with captain Brendon McCullum on 21.
TV replays suggested the Queenslander had got a slight edge but with no reviews remaining, the decision stood.
Then it got fiery, as Starc bowled like the wind with the second new ball out of shape and swapped for another – the sixth change of the test – after five overs.