With extra-time looming, GB were on the back foot as Australia pushed them back but a wonderful run and cross from Liron Mannie allowed Alfie Brooks to bundle the ball over the line.
Things got even better in the final seconds when Nick Landesberg, the manager’s son, added a fourth.
"It was a hell of a game,” said GB boss Andy Landesberg. “I believe it’s the first time we’ve beaten Australia in open futsal and it was a fantastic experience from an outstanding group of boys and physio who has worked day and night to enable them to play.
"We came here to win gold and bit by bit we got here and we saved the best till last.
"We needed everyone in the squad to win it. We had a game-plan to stifle Australia and had to be at our best. It was important we didn’t think about them too much and focus on our game. We’ve trained so hard and I’m proud of what we’ve achieved here."
Daniel Lipman was named Goalkeeper of the Tournament.
