Greig Laidlaw slotted the match-winning kick with the final play as the visitors made 129 tackles to Australia's 76 in atrocious conditions in Newcastle, New South Wales.
The win was a huge boost for a Scotland side who had lost their last seven internationals and Robinson was understandably delighted with the discipline and commitment his men showed, especially when the Wallabies had the ball.
"It's very important for the side to show the courage that we showed in defence, particularly when we turned round at half-time and it was only 6-3," said Robinson after Scotland followed up their 2009 win over Australia at Murrayfield.
"It was going to have to be an amazing effort to win the game with the pressure that Australia put us under on our line.
"We couldn't get out of our half and it needed to show a huge team spirit from everybody. I thought that was shown in abundance.
"This team has worked really hard. In the Six Nations it was unlucky in a couple of games and today it has gone the other way for us.
"We have got that bit of luck through the hard work that they put in and got a fantastic victory. Back-to-back victories against Australia for a Scottish team is immense."
Exiting the World Cup at the pool stages and picking up the Wooden Spoon in the recent RBS 6 Nations wasn't what Robinson had been hoping for at the start of those tournaments but he felt enough promise had been shown to suggest a turnaround wasn't far away.
And if the pain of defeat to Argentina and England in New Zealand and to Italy in particular back in March was hard to take, Robinson insists his squad never stopped believing in their abilities or stopped working hard to improve - an attitude that was finally rewarded at Hunter Stadium.
"I'm just delighted for the players and the management who have worked so hard," added Robinson.
"Also the Scottish supporters because it has been tough for them when the games have been so close and the team has been playing well, getting into good positions to win matches but not achieving that.
"I understand the disappointment, but for this group of players and management there is a real belief and you saw the team spirit.
"Today our plans in tough conditions worked well but we are going to have to keep improving and keep working hard. I know from the Scottish boys that they are going to do that and that is why they are a delight to coach."