Greig Laidlaw's late penalty gave the brave Scots a backs-to-the-wall 9-6 win at the Ausgrid Stadium.
The game was played in poor conditions that turned the match into a forwards orientated battle, in which the Scots' work at the breakdown was at times exceptional.
The victory over the world-ranked No.2 Wallabies also snapped a seven-Test losing streak dating back to the 2011 World Cup. It is also a big plus in Scotland's bid to move back inside the IRB top 10 rankings.
Hastings, a former Grand Slam winning centre and now a TV analyst for the game, has no doubts that even allowing for a weakened Aussie side, this was a victory to savour.
It will also send Andy Robinson's men into the final two Tests with Fiji and Samoa in buoyant mood.
Hastings said: "This was a Scotland performance full of commitment and fight. It was a backs-to-the-wall effort in poor conditions and one that has given the tourists a tremendous platform to go to Fiji and Samoa and claim a win again.
"Given the fact we had gone into this one on the back of seven defeats, you can't stress the importance of the win against the second-ranked side in the world on their patch. We have been moaning about not being able to win Tests and now that we have done it is important to savour this win.
"Success in Australia does not happen often, the last one was 30 years ago, so this is a great lift for Scottish rugby."
Hastings added: "Success at inter- national level is based a lot on confidence and momentum, and this win will have given Scotland that in spades."
The boot of Laidlaw supplied all the Scots points in the triumph – which meant a successful defence of the Hopetoun Cup – in conditions similar to those of the 2009 victory over the Wallabies at Murrayfield.
There were some huge performances, particularly from Alasdair Strokosch, whose tackling was crucial to Scotland's hopes of posting back-to-back successes over the Aussies for the first time.
The destructive scrummaging of Euan Murray at tight-head was pivotal in winning a penalty from the final scrum, which was nervelessly slotted over by Laidlaw.
But Hastings warned there were areas that must be improved if the Scots are to back up the Wallaby win with further successes in Fiji in 11 days and Samoa on Saturday, June 23.
He said: "Our throwing at the lineout was not good and caused lost ball from our set-piece that put us under pressure.
"These little errors cost us dear in the Six Nations and it is vital we eradicate them going forward. But that would be to quibble and take some gloss off a great victory.
"At the RWC, we lost a game against Argentina in similar conditions, and here against an even better side we showed that we had learned lessons from that one and got the victory we so badly needed."