Bracewell finished with 6-40 as Australia were dismissed for 233 chasing 241 to win on Day 4.
Hobart: New Zealand produced a stunning upset to win their first Test match in Australia since 1985.
Paceman Doug Bracewell finished with 6-40 as Australia were dismissed for 233 chasing 241 to win, losing their last eight wickets for 74 runs.
After a thrilling seven-run upset win, skipper Ross Taylor was quick to dedicate New Zealand's victory in the second Test as a Christmas gift to long-suffering fans.
It took a 21-year-old, second-generation Black Cap to wrap it up for them on Monday, with 21-year-old allrounder Bracewell snaring 6-40 in 16.4 overs in only his fourth Test match.
His eight-ball burst to dismiss ex-Australian captain Ricky Ponting (16), current skipper Michael Clarke (0) and veteran Mike Hussey (0) just before lunch swung the momentum decisively in New Zealand's favor after the series seemed to be drifting away from them.
In the end, only opener David Warner defied the New Zealand bowlers, carrying his bat for an unbeaten 123 in his second Test, including a 34-run last-wicket stand with Nathan Lyon that almost got Australia across the line.
The New Zealanders were thrashed by nine wickets in the series-opening match at Brisbane last week and were facing a 2-0 series defeat when Australia were cruising at 159-2 chasing 241 to win the second Test. Instead, they squared the series.
"With one wicket and 40 runs, you're favorite. When it gets down to that close ... in New Zealand cricket history, that has to go down as one of the closest, and one of the best," Taylor said. "After the way we played in Brisbane, we wanted to come down here and show a bit more passion in New Zealand and pride. And that's what we did."
"I'm ecstatic and pretty proud. Thanks to the NZ public - That was for them. We wish them a merry Christmas."
Ponting miscued a good-length ball from Bracewell and popped an easy catch to Tim Southee at extra cover to make the total 159-3, extending his drought to 31 innings since his last Test hundred.
Clarke tried to drive at an away swinger and edged to Taylor at slip and then Hussey was trapped lbw on the next ball - after Taylor asked for a review of umpire Asad Rauf's original not out decision.
Brad Haddin survived the hat-trick ball but the three quick strikes gave New Zealand the upper hand with Australia having a longer-than-usual lower order.
Bracewell was so excited he dropped a curse word into a live national radio interview, but quickly regained his composure.
"Just got to lap it in. Really chuffed," he said. "We're going to celebrate hard tonight. We hung in there tough and came out with the win ... we stayed positive and always knew we were in with a chance."
Bracewell's father, Brendon, played six Tests for New Zealand and his uncle, John Bracewell, was an allrounder and coach of New Zealand. John Bracewell was part of the 1985-86 era New Zealand squads that beat Australia at home and away.
New Zealand had a setback on the morning of the first day when veteran left-arm orthodox spinner Daniel Vettori was ruled out with a hamstring strain. But it worked out to be a positive for New Zealand, who went into the match on a seam friendly green-top wicket with four pacemen.
Bracewell took his first five wickets in two stints before and after lunch on Day Four, and Southee then claimed two wickets in an over to start the middle session as the Australians lost seven wickets for 40 with batsmen struggling to handle the late swing.
Warner's impressive performance was overshadowed by another dismal performance by Australia's top order that will almost certainly cost opener Phil Hughes his spot and raises even more questions over the Test futures of veterans Ponting and Hussey.
Even when Australia went to lunch at 173-5, it seemed the unbeaten run at Bellerive Oval would survive. But four wickets in 10 balls saw the Australians slip to 199-9.
Big-hitting Warner and Lyon whittled the target from 42 runs to single figures in a dogged stand that displayed Warner's maturity, warranting his selection.
But Bracewell quashed Australia's last chance when he bowled Lyon - who had survived two umpire reviews for lbw decisions - for nine.
The Australians had resumed on the fourth day at 72 without loss and didn't add a run before Phillip Hughes (20) was dismissed by Chris Martin for the fourth time this series - edging to Martin Guptill at second slip for the second time in the match.
Hughes was under intense pressure to hold his spot as critics targeted deficiencies in his technique outside off stump that have resulted in him being caught behind the wicket in two-thirds of his innings.
While Hughes has struggled, Warner appears to have secured his spot for the four-Test series against India starting December 26.
"Disappointed, no doubt," Clarke said of the outcome. "We were pretty inconsistent throughout this whole Test. Want to pay a lot of credit to David Warner, scoring his first Test match hundred was outstanding today. And Nathan Lyon, the way he hung in there, if a few of us batters showed the character and courage that he did today, we wouldn't be standing here with the same result."
Clarke said the main focus was already now on the next series.
"Right now, it's about being with the team and working on the pros and the cons - where we can improve come Boxing Day," he said. "We want to be 100 percent ready for the Test against India."
Warner, who made his Test debut last week at the Gabba, scored 47 from 50 balls on Sunday but took 15 further deliveries to reach 50 on Monday. He curbed his attacking instinct as his innings progressed, with his 123 coming off 170 balls and containing 14 boundaries.
"Disappointing to get so close at the end there and not getting across the line, but credit to New Zealand for the fight they put on," Warner said. "Douggie Bracewell bowled well ... fantastic effort from him and other bowlers."