Usually New Zealand does not like to glance at the trans-Tasman cricket record book.

Not winning a Test in Australia since 1985 can have that effect.

But New Zealand can dare to dream of ending their horror run after moving to 3-139 in their second dig by stumps on day two of the second trans-Tasman Test, holding an overall lead of 153.

Under pressure captain Ross Taylor (42 not out) rose to the occasion in an unbroken 66-run stand with Kane Williamson (34 not out).

And the Black Caps can already happily point to a new entry in the record books after routing Australia for 136 and taking an unlikely first innings lead.

The ghosts of Cape Town did not exactly come back to haunt them, but Australia were still reduced to their lowest total in 28 Tests against New Zealand on home soil.

Overall, it was their third lowest against the Kiwis in 52 Tests.

Reduced to 7-75 early on day two in Hobart, Australia looked on course to re-write their lowest total against the Kiwis overall - 103 set in Auckland in 1986 during Sir Richard Hadlee's heyday.

But top scorer Peter Siddle (36) and fellow tailender James Pattinson (17) combined to put on 56 for the eighth wicket to have New Zealand's suddenly healthy first-innings total of 150 in sight.

However, Chris Martin (3-46) celebrated his 37th birthday by combining with Doug Bracewell (3-20) and Test debutant Trent Boult (3-29) to complete the rout before tea.

Taylor then stood tall with the bat after coming to the crease when New Zealand had lost 2-0 to be 2-36.

And when Jesse Ryder's lazy footwork ensured he was stumped off part-timer Mike Hussey for 16, the Kiwis were 3-73 with alarm bells again ringing.

But Taylor rode his luck - he was dropped on 14 off Hussey - to finally stand tall in his third Test at the helm.

New Zealand will look to cash in on a Bellerive deck that is flattening out by the hour.