Trailing by two points at half-time but carrying momentum from a strong finish to the second period, Great Britain came out of the main break on a 14-4 run.
Terry Bywater (nine points) led the charge while Ian Sagar (26 points) proved unstoppable for most of the night.
The Rollers were able to answer with a 9-1 run of their own through Shaun Norris (14 points, five rebounds, eight assists) and Brett Stibners (nine points, two assists) but the Brits still took a seven-point lead into the final change.
Needing another run to pull off a miracle comeback, the Aussies struggled to find the basket in the fourth term, scoring just six points and shooting just 38% for the night in a frustrating offensive game.
Great Britain's disruptive defence has to be credited for most of those misses with Phil Pratt (20 points, ten rebounds, eight assists and two steals) starring at both ends of the floor.
Three offensive rebounds in the one possession before a Gaz Choudhry field goal midway through the fourth quarter summed up the game for Great Britain who ran away with it late to streak into the Semi-Finals.
It was a dour defensive slog early on with both teams feeling each other out, scoring just four points apiece in the first six minutes.
Tristan Knowles (12 points, seven boards, five assists) finally brought the crowd to life as he tracked down a wayward pass from Brad Ness (ten points, seven rebounds), flying all the way down the floor to save the ball before Norris completed the play with a lay-up.
That sparked a 9-4 run to finish the opening period and gave the Rollers some breathing space with Jannik Blair (four points, three rebounds) providing the defence with a huge rejection near quarter-time.
Stibners then hit the scoreboard in the second term for his first points and when Norris drilled a three-pointer, Australia looked to be in control.
Great Britain knuckled down defensively though, collecting a couple of crucial stops which swung the momentum and while Shawn Russell hit a buzzer-beater right on half-time, that momentum for the Brits would prove game-changing.
The full box score can be found here.
A heartbreaking end to their 2016 Paralympic medal hopes is not the end of the Rollers' tournament though as they will play the loser of Turkey/Brazil in the 5-6 classification game.
That contest will tip-off at 4.15am AEST Sunday morning.