Ross Taylor's become the first New Zealand cricket captain to lead the Black Caps to a test win in Australia since 1985 when Jeremy's Coney's side won the series there.
The young pace bowler Doug Bracewell took six for 40 as Australia collapsed to 199 for nine and was eventually dismissed for 233, chasing 241 to win the second test in Hobart and the series 2-0.
But although it looked as if the seven run win would be more decisive opener David Warner, who was unbeaten on 123, added 33 for the last wicket with Nathan Lyon before Bracewell bowled Lyon for nine.
Taylor says they got Australia too close for the good his heart-rate in a match which will have to go down as one of the closest and best with the Black Caps showing a lot more pride and fight than they did in the big loss at Brisbane.
New Zealand's last test win over Australia was at home in 1993.