Andy Robinson’s side produced a monumental defensive performance at Hunter Stadium in Newcastle to claim an attritional battle with the final kick of the game from Greig Laidlaw.
It ends a run of seven straight defeats for the Scots, and is their first win over the Wallabies in Australia since 1982.
A severe weather warning on Tuesday morning in the Newcastle area did not prevent the staging of the opening match of Scotland’s three-Test tour of the South Pacific.
With torrential rain and gale-force winds buffeting supporters and players alike, it was never going to be a game peppered with running rugby.
Scotland had the wind with them in the first half and immediately put their hosts under pressure, with Mike Blair the first of many in the game to spill the ball forward at a crucial moment near the try-line.
After Joe Ansbro’s powerful run was halted, Australia turned the ball over and sought to kick clear – but the ball went up and not forward. They knew then they were in for a long half.
Australia, who were also ‘bushwhacked’ by Samoa in the opening match of the last Test season, were missing influential fly-half Quade Cooper as well as regular stars Kurtley Beale, James O'Connor and James Horwill.
That meant flanker David Pocock was captaining the side for the first time, and he led by example at the breakdown, disrupting play and using up the time.
Will Genia was caught out by the weather as a Scotland up-and-under fell to earth, but wing Joe Tomane, who earlier almost led a break from deep in his own half on the right, was there to recover the ball under heavy pressure.
Laidlaw kicked the opening points on 23 minutes as the Wallabies’ discipline let them down and when Tomane again went off his feet in the ruck five minutes later it was 6-0 thanks to the fly-half’s boot.
Full-back Stuart Hogg lost the ball from the kick-off and Australia pressured Scotland in their own half. When Scott Higginbotham failed to take a Genia offload cleanly near the try-line play was pulled back for a penalty, and Mike Harris drilled it over to take them in at half-time only three points down.
Australia actually had the majority of the territorial possession in the final quarter of the half, but Scotland played almost the entire second period in their own backyard.
Things looked ominous when Ross Rennie was almost immediately penalised for holding down Genia and Harris curled another impressive kick over – again he had a team-mate holding the ball in place for him, so high were the winds.
And when the restart was sent straight into touch, Robinson was left pulling out whatever remains of his hair.
But his men made amends with a brilliant defensive showing from there which left Australia at a loss for ideas.
On one occasion, on 55 minutes, Australia replacement Rob Simmons thought he had a try, but the video referee could not confirm that he touched the ball down amid a mass of bodies.
Harris twice tried to kick for goal from halfway, the ball dropping well short on both occasions, and he was culpable for giving Scotland the chance of the win.
He went for a monster drop-goal from his own half which ran over the dead-ball line, allowing Scotland a scrum between halfway and the home 22. They used up the remaining four minutes impressively before looking to get Laidlaw back in the pocket.
They thought they had a penalty as Australia turned a scrum around, but another scrumdown was awarded; and on that one South African referee Jaco Peyper did spot an infringement.
Laidlaw sent the ball over from just outside the 22 to spark wild celebrations among the Scotland players and staff.
Scotland will play Fiji in the early hours of Saturday June 16 (UK time) then Samoa, again early in the morning, the following Saturday.