New Zealand captain Ross Taylor admitted he "nearly had a heart attack" as Australia's last pair threatened to deprive his side of a first Test win over their rivals since 1993.
The Black Caps prevailed by seven runs - their narrowest Test win, and equal seventh in the format's history - after David Warner, who carried his bat for an unbeaten 123, and Nathan Lyon almost took the hosts over the line in Hobart.
The latter was bowled by a fine Doug Bracewell inswinger though, to become the rookie paceman's sixth wicket and end a stand of 34 with Australia eight short of their victory target of 241.
"They fought the whole way," Taylor said afterwards. "We would have won by 40 runs out there against some teams but the way Lyon and Warner played, I nearly had a heart attack.
"Warner was outstanding. To come in in only his second match and control the game the way he did... we'll be on the wrong side of a few hidings so I can't feel too sorry for him, but he deserves a lot of credit for the way he batted."
The 21-year-old Bracewell has only one more Test to his name than Twenty20 specialist Warner, and Taylor said: "I'm just stoked for Dougie.
"He bowled outstandingly well for a young guy, 21 and in only his third Test to get Ponting and Clarke and Hussey - that's something to tell your grandkids about.
"The way (Peter) Siddle and (James) Pattinson bowled from that end - Dougie is probably 5kph slower than them but he's a similar bowler. As captain you've got to go on hunches - I thought Doug would bowl well, I didn't think he'd bowl that well."
Taylor had just turned nine years old the last time New Zealand beat Australia, while their last win across the Tasman was in 1986.
And the captain said: "Rugby is our number one sport but any sport against Australia, winning in Australia, the New Zealand public enjoys.
"The New Zealand public knows that the New Zealand cricket team, when playing against Australia, is always the underdogs, but they don't like it when we don't show much fight. That's what we didn't do in Brisbane. We showed a lot of ticker today."
Australia's narrow defeat follows a similarly tense conclusion to the series in South Africa, where teenager Pat Cummins saw them over the line for a two-wicket win in Johannesburg to tie the series.
And captain Michael Clarke said: "We see the other side of Joburg today. We were on the winning side in South Africa, today we just missed out.
"It probably sums up where we're at as a team, you've seen some really good patches of individual excellence and as a team we're playing really well in patches, but then you see the other side as well where we're letting ourselves down by very poor performances."
Warner, reflecting on his maiden Test hundred, said: "To achieve a milestone like that's always fantastic, but at the end of the day we lost and it's more disappointing to be out there with eight runs to go and not get across the line."
But he had nothing but praise for number 11 Lyon, adding: "I batted with Nath in Zimbabwe this year and he hit the winning runs over there, we had to get 30 runs there as well.
"Doug Bracewell bowled well and it shouldn't have come down to Nathan anyway."
While Warner took the plaudits, opening partner Phil Hughes came under pressure after scores of four and 20 left him with just one half-century in four Tests across the New Zealand and South Africa series.
And Clarke hinted at a change at the top of the order when he said: "Hughesy's been getting out the same way, he's been working really hard in the nets to try to improve that deficiency in his technique.
"He needs to find some runs, if he's not making them for Australia he's going to have to go back and score some for New South Wales."