Latham, Ross Taylor, Brendon McCullum and Jimmy Neesham then fell in quick time, two apiece to the Mitchells.
Kane Williamson, batting impressively was on 55 and BJ Watling had reached 14.
It was a second grim day for New Zealand who, in addition to shipping another 167 runs while taking two wickets, lost the services of their bowling spearhead, Tim Southee.
He walked off having bowled five overs today with an irritated disc in his back.
It thrust extra work onto the other bowlers, none of whom had impressed on day one, and only Trent Boult, with a much improved display in the first session today, stood out.
Left armer Neil Wagner is flying across to join the squad as cover for Southee ahead of the second test starting in Perth next Friday.
By the time Australia declared, they had run up three 150-plus run stands in the innings, Usman Khawaja had turned his maiden test century into 174 and the last time Australia's first four wickets had scored more than 556 runs was in 1993.
Khawaja began the test with a question mark over his place in the side. He answered it emphatically, albeit against a less than truly demanding attack.
Adam Voges struck an entertaining unbeaten 83, helping add 157 with Khawaja to help cement his place in the batting order.
Good points for Australia to savour, which is a luxury New Zealand don't have right now.
SCOREBOARD