With just under four minutes to go, the visitors clawed their way back to trail 36-30 to show the composure which earned them the pre-season Loggins-Bruton Trophy of the ANBL Blitz in Victoria this month.
The teams went into the locker room at halftime with Breakers centre Alex Pledger beating the buzzer to draw a foul off a rebound, before breaking the deadlock for a 40-38 lead from the charity line but that spell belonged to Melbourne (19-12).
Dominican Republic import point guard Edgar Sosa, who sat out the ANBL Blitz tournament last week due to injuries, spearheaded the points for Breakers with nine while Ili added eight. Pledger, Thomas Abercrombie and Finn Delany chimed in with five each.
Forward Delany (4) and Pledger (3) showed their worthiness on rebounding.
For Melbourne United, guard Chris Goulding led the charge with 12 points predominately from field goals while forward Casey Prather added to the total with seven points.
Centre Josh Boone (4), forward Craig Moller and Tall Black forward Tai Wesley (three each) took care of the boards.
When play resumed in the third spell, Melbourne snuck 49-48 ahead but the loudest noise came from Pledger blocking import point guard Casper Ware jnr only to have Wesley shut out Ili on counterattack.
That lead didn't last as the Breakers nudged ahead 51-50 past the five-minute mark in what had all the promise of a tit-for-tat match.
The blood pressure of Henare and Vickerman had started rocketing by that stage.
With just under three minutes left, import power forward Majok Majok asked questions of the Breakers ' defence when he regathered three times for a two-pointer off the glass to push his side ahead, 58-53.
The Breakers finished with a field goal but that quarter belonged to a pumped-up Melbourne (22-15) as they led 60-55.
The tempo of the game increased, as expected, in the final quarter when American import guard Devonte Newbill, who was having a quiet first half with 14 minutes on the floor, came to life.
Four minutes into it, the Breakers pushed ahead 67-64 as Vickerman called timeout.
The game was locked 70-70 with 3:30 minutes left on the clock as the crowd were treated to some Newbill magic as he drew a foul before dropping two points from the free-throw line to end the impasse.
Breakers centre Rob Loe, who Henare had benched after eight minutes in the first quarter, returned in the final spell to muscle up for a few points and get into the face of Wesley.
With the Breakers ahead 76-75, Low drew a body-slamming foul from Goulding and a basket, much to the dismay of Vickerman and his howling bench, to push the score in the hosts' favour, 80-75.
The crowd found their voice as a bloke with a microphone got the 70 per cent-capacity PG Arena into chants of: "Let's go Breakers, let's go!"
With the Breakers leading 83-79 and less than a minute to go, Ili and Sosa bounced, passed and faked for time to draw a foul, which Sosa dropped from the free-throw line.
But Loe gave away a needless opportunity when he pushed a shot from under the hoop that might have rimmed out.
Melbourne United converted from the charity line to narrow the deficit to 85-83 with 20 seconds left but the Breakers hustled to extend the lead to 87-83 with 10 seconds remaining.
However, Prather wasn't done, dropping one from the carpark to leave the game on a tantalising edge as they nipped at the Breakers' heels, 87-86, with six seconds to play.
It was Newbill's turn to draw a foul but he could only land one point, 88-86, as Henare pulled out Delany and injected Jordan Ngatai.
Casper had a chance to tie the game but came up shy under the basket for the Breakers to clinch the final spell 33-26 and, quietly, the bragging rights.
Sosa finished with a game-high 21 points with Ili adding 14, Delany 13 and Pledger 11, including eight rebounds.
For Melbourne, Goulding top scored with 18 points with Prather adding 16, Ware jnr 14 and Wesley 13.
Josh Boone, Moller, Majok and Wesley shared board duties although, akin to the Breakers, no one stood out as assists king.
The hosts scored 41 points off the bench compared with Melbourne's 18.
The Breakers' posted the biggest lead of 15 (36-21) and the visitors seven (60-53) but the latter chalked up the biggest scoring run of 12 points (33-36) in a game where the scores were tied 10 times and and the lead changed hands nine times.
The Breakers will face Melbourne in New Plymouth on Tuesday before hosting the Brisbane Bullets in Tauranga on September 27.