Scotland's season ended in defeat as Australia, inspired by two more tries from Lote Tuqiri, completed a 2-0 series sweep over Matt Williams' developing side.
Tuqiri scored twice in the Wallabies' 35-15 victory in Melbourne last Sunday and was again the thorn in Scotland's side as Australia ran in five scores in all.
Scotland turned in another proud display and a first Test try from scrum-half Chris Cusiter brought them to within seven points at the interval after quickfire scores from Wendell Sailor and Tuqiri had opened Australia a 17-3 lead.
The tourists often lacked the courage of their convictions in attack and the more clinical execution from the Wallabies proved telling.
Tuqiri scored his second after the interval, followed by a third Test try for Morgan Turinui while Joe Roff crossed with the final move of the match to finish with 14 points.
Scotland had not beaten Australia since Andy Irvine's side invaded Ballymore in 1982 and in the 12 matches since they had conceded fewer than 30 points on only two occasions.
Although Scotland had taken heart from their performance in last week's defeat - particularly in defence - they needed to conjure more attacking options to threaten the Wallabies.
Dan Parks, who finished with eight points, exchanged penalties with Roff before Scotland were given the chance to work it through the backs.
Unfortunately, when the overlap finally came, with Parks sending a raking ball out to the wing, it was Murray who was waiting and the lock forward did not have the pace to beat the scrambling defence.
Tuqiri then burst down the short side for Australia before Stephen Larkham sent a long ball across the backline to David Lyons who knocked on under pressure from Simon Webster.
But from the ensuing scrum, Scotland were shoved off their own ball, Larkham broke through Jon Petrie - on as a blood-bin replacement - and Donnie MacFadyen before handing over to Sailor to score under the posts.
Australia's second try followed just four minutes later when Phil Waugh and Radike Samo combined to pinch the ball at the breakdown, Samo then embarked on an elusive trademark run and Scotland paid for failing to bring him to ground.
Morgan Turinui spread the ball through Larkham and Lyons to Tuqiri, one of two Australians basking in space on the wing, and eight minutes before the interval the Wallabies had stretched their advantage out to 17-3.
But Scotland hit straight back. First they thought Andy Henderson - Scotland's stand-out player - had scored when he burst through, only for referee Mark Lawrence to award a five-metre scrum after he had inadvertently blocked George Gregan's path.
The Scots got the try their endeavours deserved when Cusiter snuck over from the breakdown for his first Test score.
It was converted by Parks who then missed another penalty shot with the final kick of the half as Australia carried a 17-10 lead into the changing room.
The Scots continued that momentum after the interval with Iain Fullarton bursting through the Australian ruck and charging 20 metres before the Wallabies sucked up the pressure and forced Scotland onto the back foot as Roff had charged down Southwell's clearance.
Turinui then cut through the Scotland defence and the ball passed through Brendan Cannon and Roff before Tuqiri touched down for his second try.
Scotland introduced Craig Hamilton for Fullarton with the Newcastle man winning his debut cap.
They were battling valiantly and then almost created their own score straight from the line-out when Bulloch threw to Jason White at the front and he raced from the 22 to within inches of the line before Sailor hauled him down.
Scotland could not convert the chances and overlaps into maximum points and then had to settle for a second Parks penalty to move within nine points of Australia.
The game was secured for Australia when Turinui, making the most of his unexpected start, ran hard and straight through two feeble tackles to score his third Test try under the posts.
Nevertheless, Scotland's spirit was strong and they continued to press, but charges towards the line from Hinshelwood, Bulloch and Tom Smith were all repelled.
There was still time for the killer blow and Roff spun over the line to score with the final move of the game and send Australia into next week's World Cup final rematch against England on the back of successive victories over Scotland.