"It was pretty simple really. I stayed patient, kept the ball in the right areas and didn't do anything too spectacular," he said on the eve of the three-test series starting in Brisbane on November 5.
"I felt I've bowled better than that, but not taken a bag of wickets. It was just one of those days (the second Australian innings) and the ball was coming out pretty nice.
"We ended up coming out on top which was fantastic but this time they're going to be tough and we're going to have to be on top of our game."
That performance appeared to have set Bracewell up for a longterm place in New Zealand's test XI, but it didn't work out that way.
In 19 tests, he's taken 55 wickets at 35.1 but was rubbed out of the test frame for several months, for off-field indiscretions with Jesse Ryder before the start of the home series against India early last year.
Now he's back and effectively in a duel for the third seamer's spot for the opening test at the Gabba with Canterbury seamer Matt Henry, as support for new ball pair Tim Southee and Trent Boult.
He warmed up for the tour with five for 67 against Otago on the batting highway at Napier's Nelson Park last week and insists he's a wiser bowler now than he was last time he was in Australia.
"Absolutely. I feel like I'm getting better all the time, and obviously a lot more experienced, being around the guys for a few years. Each day I try to learn and get better."
Bracewell has one point in his favour: he's played test cricket in Australia, has experienced the grounds, the conditions and the crowds, and he's had success.
Henry is the incumbent from the second test win over England at Leeds in May. The contest shapes up as among the most intriguing selection aspects ahead of the first test.