Andy Robinson's men went into the match at Murrayfield as substantial under dogs having failed to beat the Wallabies in 27 years before an heroic defensive display resulted in a 9-8 victory for the home side.
That moment of glory was so nearly snatched from them, however, as an injury-time try from Ryan Cross gave Aussie kicker Matt Giteau the chance to rescue Robbie Deans and co with the final play of a pulsating encounter.
But even when Giteau looked set to deliver the cruelest of blows, Godman says he still believed it would be his and Scotland's day.
"At the end it was a bit surreal to be standing behind the posts thinking we had held them out for two or three minutes on our line," said Godman, who kicked two penalties to help Scotland on their way.
"Some guys were jumping about to charge the conversion but I was shattered and standing there in a daze.
"At the back of my mind, though, I knew the wind was blustery and there had been a few misses already.
"The first time I took a penalty in the second half I hit it straight down the middle and was surprised to miss.
"The next one I started quite a bit right and I thought it might sneak in at the right hand post but it actually rebounded over off the left-hand post.
"Even in my shock I could afford to be a bit hopeful."
Godman himself was voted man-of-the-match for his commanding all-round display but the 27-year-old was far more interested in the overall performance of entire Scotland 22.
The capital-city playmaker certainly enjoyed the winning feeling that came as the reward for such an outstanding team performance and he is now determined to ensure that feel-good factor continues when Scotland face Argentina this weekend.
"At the end of the game I was so shellshocked, so knackered I could hardly take in the man-of-the-match announcement," added Godman.
"It's nice and I'm sure my mum and dad, who have been very supportive, will find a place of honour for the man-of-the-match trophy.
"But winning is what we were there to do and any individual honour was for the team.
"There were others who stood out for me including both our scrum halves, Chris Cusiter for the way he started and then Rory Lawson after he took over and proved outstanding.
"To have Mike Blair, who missed out through injury, sitting in the stand added to the feeling that we have three world-class scrum halves of exceptional quality and that depth contributed to beating Australia.
"Any level of rugby, but especially internationals, is all about winning. That's where you get your confidence from and that will help with a really hard game coming up against Argentina.
"We now need to back up successes against Fiji and Australia against opponents who will be very dogged."
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