In torrential conditions at the Hunter Stadium, Scotland were under the cosh for the majority of the match but some heroic defence kept Australia at bay.
Scotland had led 6-3 at halftime after Laidlaw landed a brace of penalties and although Mike Harris brought Australia level, an offence at the scrum gave the Edinburgh half-back the opportunity to make himself a hero.
It was a chance the 26-year-old seized as Scotland banished memories of their Wooden Spoon in the Six Nations.
The victory was all the more impressive for a side featuring debutants in the form of Edinburgh full-back Tom Brown, centre Matt Scott and Glasgow prop Ryan Grant - all of whom had made their mark in the RaboDirect PRO12 this season.
And Laidlaw reserved special praise for the front row's gritty performance.
He said: "One to 15, the guys were absolutely outstanding," said Laidlaw. "They defended as a team, as a sort of blue wall across the park.
"That's something we have talked about as a team, and personally I've been working hard on it. I like to think it's been coming through.
"When we look back on the game, the defence has won it for us.
"It was really a kick for the guys in the scrum because before that they were outstanding to force the penalty.
"It was probably the toughest kick I have ever had from in front of the posts. I was slightly worried about the weather because it was pretty messy all night.
"But I was delighted when the ball went through the posts at the end."
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