A last-wicket partnership of 34 runs between opener David Warner, who powered his way to 123 not out, and Nathan Lyon (9) threatened to wrestle the match back to Australia before Bracewell struck with the winning blow, clean bowling the latter for nine.
"There was a period before lunch and just after where it was very tense and close and to come out and win it was amazing. It showed true fight within the team," Southee said.
When Lyon's wicket fell and the Black Caps realised they had finally broken the 26-year hoodoo of not beating Australia on their home soil, Southee said he felt relief.
"But then, there was just excitement. For some of these guys it is the greatest achievement of their careers and it is a day to remember for the rest of our lives. It's amazing to be part of something so special - five or six guys in the team [including the 23-year-old Southee] weren't even born when New Zealand last beat Australia at home," Southee said.
For Southee, personally, the win was special. "I've only had two test wins in 15 games but it is one of the highest personal achievements I have had and to be part of this team which beat Australia - a lot of great cricketers have come to Australia and haven't been able to do that ... it's up there as one of the best days of my life," he said.
After their disappointing first test loss in Brisbane just days before, Southee said the side did a lot of soul-searching and entered the second test with a point to prove. "It was a never a matter of not having the talent or ability to beat Australia. We backed ourselves and we were lucky we got the chance to do it all over again. It was courage and determination that got us there ... but we were a bit embarrassed I guess after the first test and we had a point to prove to ourselves personally."
After the victory, which skipper Ross Taylor dubbed as an early Christmas present for the team and fans (and birthday present for Southee, who turned 23 on Sunday), the team sat in the changing room for five or six hours, reflecting on the game and enjoying each other's company over a few beers, Southee said.
"Then we continued on until the early hours of the morning. There will be a few sore heads around," he quipped.
Although they had self-belief to start with, this win will surely add fuel to the the Black Caps fire, and Southee said he and his teammates are keen to continue their winning momentum. "We are just a young team and, hopefully, we will be playing together for a few more years yet," he said.
The Black Caps team return today and Southee said he was looking forward to spending Christmas at home before playing in the domestic HRV Twenty20 Competition for the Northern Knights.