Cricinfo said the Black Caps owed their win to the "extraordinary" bowling of Doug Bracewell and a "horrific" batting disintegration from Australia.
It said the win showed Bracewell was a bowler of enormous potential.
The local Tasmanian newspaper, the Mercury, likened Australia's batting order to Russian roulette saying the crumbling order contributed to an "embarrassing loss" at Bellerive oval, Hobart.
"A maiden Test century from David Warner could not save Australian blushes and even more confusion over the make up of the side going forward," it said.
It added that Hughes was destined for the axe after failing to add to the scoreline from the previous day's play.
Actress Madeleine Sami tweeted: "Black caps you beauties! #nicetobeinozzierightnow."
The Managing Director of the Australian Broadcasting Corporation Mark Scott said: "About to have a meeting with a member of the executive who is a New Zealander. The timing could be better. #abchobtest"
Others took the opportunity to rail against the decision to name Australian centurion David Warner man of the match.
Max Johns said: "Warner man of the match? This is what happens when you let the audience at home vote BEFORE the end of the game #blackcaps"
Andrew Biggs said: "Let's have a #BlackCaps twitter-fan whip round to reward the REAL man of the match Doug Bracewell #illputintenbucks"
- Herald online