The Black Caps claimed eight wickets for 74 runs to claim a dramatic victory midway through the fourth day of an extraordinary Test match at Bellerive Oval.
Bracewell finished with 6 for 40 off 16.4 overs in a match-winning performance to stun the Australians, who appeared on track for victory at 159 for 2 chasing 241 runs to win.
But the Australians folded spectacularly and David Warner's unbeaten maiden Test century went in vain as wickets tumbled around him and last man Nathan Lyon was bowled by Bracewell in the 64th over to claim victory.
It was the Black Caps' first victory in Australia since 1985 and they tied the two-Test series after comprehensively losing the first Gabba Test by nine wickets.
Bracewell turned the match around with the wickets of Ricky Ponting (16), Michael Clarke (0), Mike Hussey (0), James Pattinson (4), Mitchell Starc (0) and Lyon (9).
Warner finished unbeaten on 123 off 170 balls with 14 boundaries to cement his position in the Test side after fellow opener Phillip Hughes was out again cheaply.
Warner edged out Bracewell as official man-of-the-match in a television viewers' poll.
The Australian reached his century when he tucked Bracewell behind square leg for two shortly after lunch and greeted his achievement with a leap into the air and a kiss on his helmet.
But wickets continued to fall with Brad Haddin snapped up by Ross Taylor in the slips off Tim Southee and Peter Siddle taken at third slip off Southee for two.
Bracewell removed Pattinson and Starc within three balls to have the Black Caps one wicket away from a remarkable win as last man Lyon came out to join Warner after Australia had lost seven wickets for 40.
In a tense climax, Lyon survived two reviews for lbw as Warner went after the runs against a spread-eagled field.
But Bracewell finished the game when he bowled Lyon in the 64th over to jubilation among his teammates.
Ponting's possible final Test innings in Hobart finished in a whimper after he was given a standing ovation to the wicket from the small crowd.
Test cricket's third-highest run scorer spooned a catch to cover after playing back to Bracewell and was out for 16 to complete a poor match after scoring just five in the first innings.
Clarke was caught at slip by Taylor and Hussey was out first ball lbw after a review went in bowler Bracewell's favour.
Hughes's Test future again looked uncertain after he was out in the day's second over with no addition to his overnight score of 20.
It was the fourth straight time Hughes was caught by Martin Guptill in the slips off Chris Martin's bowling in the series.
His latest batting failure -- 41 in four innings against the Kiwis -- will intensify the pressure on his spot ahead of the Test series with India, starting at the Melbourne Cricket Ground on Boxing Day.
While Hughes's technical deficiencies outside off-stump continued to hound him, his fellow New South Wales left-hander Warner built a strong case for his retention, possibly partnering Shane Watson against India.
Usman Khawaja again failed to go on after getting a start and went to drive Trent Boult only to give an edge to Taylor at first slip. Khawaja made 23 off 48 balls.