With NBA guard Patty Mills contributing a game-high 20 points, as well as five rebounds and four steals, the Boomers turned around some poor first-half shooting that had them trailing 39-32 at the main break.
It made for a winning return for Boomers coach Andrej Lemanis to the North Shore Events Centre, the home venue of the New Zealand Breakers, whom he guided to their unbroken run of three NBL titles.
With the teams both already knowing they are both bound for next year's World Cup in Spain, the stakes might not have been as high as for a sudden-death qualifier.
But the intensity of the contest lived up to the traditions of trans-Tasman rivalry.
The Tall Blacks, underdogs heading into the two-match series, showed plenty of spirit, with skipper Mika Vukona leading the way.
But when their early shooting accuracy dipped at the start of the third quarter, the Boomers took advantage to move into a lead they wouldn't relinquish.
A seven-point run, including five from Mills, nudged the visitors in front.
Up 54-52 at three-quarter time, Australia lifted a gear in the final quarter to pull away.
David Andersen was a key contributor to their cause, finishing with 12 points and seven rebounds, while Matthew Dellavedova added 11 points.
Corey Webster led the scoring for the home side with 14 points, while Vukona had 11 and eight rebounds.
Earlier, a seesawing first quarter ended in Australia's favour 21-18 thanks to a late three-pointer from Ryan Broekhoff.
But that was to be last points the Boomers scored until almost halfway through the second quarter as their field goal shooting fell to 25 per cent at one stage.
Some tight defence and two long-range buckets from veteran Casey Frank pushed the Tall Blacks in front.
The Boomers finally managed to get going again when Anderson finally replied with his own three-pointer to tie the contest.
But New Zealand finished the half stronger, Vukona providing impetus with two tough two-pointers in a row.
Webster then produced a late flourish, following up a three-pointer with another basket to give the home side a seven-point halftime lead.
The second leg is in Canberra on Sunday.
Earlier, Lauren Jackson lived up to her top billing to guide Australia to a comfortable 66-50 win over New Zealand to put the Opals within sight of qualifying for the women's world basketball championships.
The classy centre was a dominant presence with 22 points despite coming back from a lengthy injury lay-off.
The trans-Tasman rivals meet again in the second leg of the Oceania championship on Sunday, with the series winners clinching a berth at next year's world tournament in Turkey.
Australia, the world No.2, were hot favourites going into leg one in Auckland on Wednesday night.
Their roster includes four players, Jackson among them, who won bronze at last year's London Olympics, while New Zealand were fielding six new caps.
The Opals were never headed during the four quarters at the North Shore Events Centre.
Jackson made her mark from the start, a nonchalant three-pointer an early contribution in her 26 minutes on court.
Natalie Hurt chimed in with 12 points, while Mariana Tolo scored eight.
The Tall Ferns showed plenty of fighting sprit in the opening half to stay in touch, with co-skipper Toni Edmondson producing an energetic performance.
Edmondson finished with a team-best 18 points and pulled in a game-high six rebounds.
The next best of the New Zealand scorers were co-captain Micaela Cox and Test debutante Megan Craig with eight each.
Australia, up 34-26 at half-time, made their big move early in the third quarter, which they opened with 11 unanswered points.
From there, it was a case of how much the Tall Ferns could restrict the final margin and they stuck well to the task in the fourth quarter.
A late setback meant New Zealand went into the match with an 11-strong squad, after a seventh uncapped player, guard Kate Fielding, was sidelined on eligibility grounds.
The Australian-born 27-year-old, who plays for the West Coast Waves under Tall Ferns coach Kennedy Kereama, has a New Zealand father and New Zealand passport.
But Fielding was told by world body FIBA that she had to have declared her basketball allegiance to New Zealand by the age of 16.
That meant she was a restricted player, of which teams are allowed only one, and Kereama gave the nod to American-born Casey Lockwood.