Great Britain had the edge in the early exchanges but Australia opened the scoring after 29 minutes when Ben Hornby intercepted a loose pass on his own try line and sent Greg Inglis in under the posts at the other end.
But the Lions hit back almost immediately when half-back Sean Long, who was behind much of Britain's best work, dummied his way through some static defending to put Paul Wellens over for a try and send the two sides in level at half-time.
Long came out for the second half with a heavily bandaged head to protect a gash over his right eye from a late challenge by second-rower Willie Mason for which he was placed on report.
It was Mason's second moment in the spotlight, in the third minute he punched Lions' prop Stuart Fielden to the ground giving away a penalty.
A controversial decision by the video referee to put Britain ahead for the first time early in the second half. Lions captain Jamie Peacock carried four defenders over the line but replays seemed to show that he had lost control of the ball before reagthering it when it bounced off an Australian arm.
Australia threatened two minutes later but Willie Mason dropped a pass from skipper Darren Lockyer with only Wellens between him and the try line.
Lockyer had begun to take control of the game and he scored his team's second try in the 52nd minute to level the scores at 12-12.
|Willie Mason (L) tries to brush off|
a tackle by Britain's Keith Senior
But instead of buckling the Lions dug in and winger Gareth Raynor saved a certain try when he knocked the ball out of Ben Hornby's hands as the Kangaroos' scrum-half was about to ground the ball.
Four minutes later Lee Gilmour surged through two tackles to put Great Britain in front again at 18-12 Long had two attempts to put his team further ahead but he missed with penalty goal and drop goal attempts.
Long was instrumental again three minutes from time when he regathered his own kick to give Great Britain possession deep in Australia's territory. From the next play, centre Kirk Yeaman put his Hull team-mate Raynor over to seal the victory before Long added a late field goal.
"It took a great performance to win," said Britain's Leon Pryce.
"They are recognised as the best in the world, so to beat them is very special."
Lockyer admitted that his side had made too many mistakes.
"We made some errors at some crucial areas of the game," he said. "In the end that's what killed us ... but they were a committed side and they played really well."
The victory, Britain's first on Australian soil in 14 years, puts them second in the Tri-Nations table behind the Kangaroos who have already qualified for the final.
Great Britain play New Zealand next Saturday in Wellington with the home side needing to win to stand any chance of qualifying for the tournament's final on November 25. The Kiwis beat the Lions 18-12 last time out but the points from that game were taken away after it emerged they had fielded an ineligible player.