Scotland recorded their first ever win over Australia in Sydney when they beat then 24-19 on Saturday.
The teams scored three tries each, but the boot of Finn Russell - who scored 14 points with a try, three conversion and a penalty - proved the difference.
Scotland dug deep to pull off a famous victory over in a gripping international.
Scotland were ahead 17-12 at half-time and after regaining the lead midway through the second period, they held on gamely for the win.
Fifth-ranked Scotland proved the nemesis of the Wallabies, the world No.3, and won again in Australia after a try-less 9-6 victory on their last tour in Newcastle in 2012.
In a tight finish, the Wallabies tried desperately to conjure the converted try needed for victory but the Scottish defence refused to buckle.
Scotland have given the Wallabies plenty of trouble in recent years and heading into the Sydney Test had gone down by just one point in their previous two meetings.
The Wallabies were their own worst enemies in a ragged first half, gifting the Scots two tries to trail at half-time as Israel Folau replied with two signature tries, making it four in his last two Tests.
Scotland had the better of the early exchanges and fullback Greig Tonks gave them the lead with a long-range penalty goal.
Australia were sloppy in possession and a poor pass from scrumhalf Will Genia to hooker Tatafu Polota-Nau was snapped up by inside-centre Duncan Taylor, who ran over from 30 metres.
Flyhalf Finn Russell's conversion gave the Scots a surprise 10-0 lead after 15 minutes.
But the Wallabies hit back minutes later when Bernard Foley found Folau with a huge gap out wide for the fullback to storm over.
Foley's conversion narrowed the deficit to 7-10 with 20 minutes gone.
But yet again Scotland feasted on a Wallabies mistake when the influential Russell charged down Genia's clearing kick to score another gift try.
Russell converted his try and the Scots were threatening an upset at 17-7 after 27 minutes.
The Wallabies answered with a breathtaking second try for Folau, who easily out-jumped Tonks to score off Foley's pinpoint cross-field kick to the right wing.
That left the Wallabies trailing 12-17 at half-time but they returned with more intent and ripped into the Scots with some ferocious tackling.
Stephen Moore replaced Polota-Nau 10 minutes into the second half and Australia hit the front 19-17 when Genia burrowed over for a try from a ruck on Scotland's try-line after 57 minutes.
But the Scots roared back with a well-taken try to openside flanker Hamish Watson, after winger Lee Jones leapt over an attempted tackle, as Scotland outnumbered the Australian defence.
Scotland held out the Australian offensive and got a scrum feed when they held up a Wallabies surge deep inside their quarter as the clock ticked down.
Yet another Wallabies opportunity was thrown away when lock Rory Arnold lost the ball in a line-out close to Scotland's line.
Man of the match: Bernard Foley was not perfect, but directed the Wallaby show adequately. Israel Folau, with two tries and a bucketloads of superior skills, was by some distance Australia's best player. Lots of Bravehearts, but flyhalf Finn Russell was the general that drove the Scottish forward into battle - and our Man of the Match.
Moment of the match: This one goes to the Israel Folau try right on the stroke of half-time - a perfectly timed cross-field kick by Bernard Foley - with Folau leaping like a gazelle to pluck the ball out of the air and score. It was a fine display of Folau's amazing skills.
Tries: Folau 2, Genia
Cons: Foley 2
Tries: Taylor, Russel, Watson
Cons: Russel 3
Yellow cards: Bernard Foley (Australia, 24 - foul play, late shoulder charge), Rayn Wilson (Scotland, 38 - repeated infringements, killing the ball at the breakdown)
Australia: 15 Israel Folau, 14 Dane Haylett-Petty, 13 Tevita Kuridrani, 12 Karmichael Hunt, 11 Eto Nabuli, 10 Bernard Foley, 9 Will Genia, 8 Scott Higginbotham, 7 Michael Hooper (captain), 6 Ned Hanigan, 5 Adam Coleman, 4 Sam Carter, 3 Allan Alaalatoa, 2 Tatafu Polota-Nau, 1 Tom Robertson
Replacements: 16 Stephen Moore, 17 Scott Sio, 18 Sekope Kepu, 19 Rory Arnold, 20 Richard Hardwick, 21 Joe Powell, 22 Quade Cooper, 23 Reece Hodge.
Scotland: 15 Greig Tonks, 14 Lee Jones, 13 Alex Dunbar, 12 Duncan Taylor, 11 Rory Hughes, 10 Finn Russell, 9 Ali Price, 8 Ryan Wilson, 7 Hamish Watson, 6 John Barclay (captain), 5 Jonny Gray, 4 Ben Toolis, 3 Zander Fagerson, 2 Fraser Brown, 1 Gordon Reid
Replacements: 16 Ross Ford, 17 Allan Dell, 18 Willem Nel, 19 Tim Swinson, 20 Josh Strauss, 21 Henry Pyrgos, 22 Ruaridh Jackson, 23 Matt Scott
Referee: Wayne Barnes (England)
Assistant referees: Matthew Carley (England), Brendon Pickerill (New Zealand)
TMO: Shane McDermot (New Zealand)
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