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With the wind and rain making any sort of attacking rugby virtually impossible, the Scots stood up magnificently to a barrage of Australian attacks in the second half, before a scrum penalty with the 80 minutes up gave Laidlaw the kick for victory.
From slightly to the left on the Australian 22, the Edinburgh fly-half was never going to miss, and duly gave Andy Robinson his first win since a 15-6 success over Georgia in the World Cup.
The Scots had made the better start but despite some concerted pressure on the Australian line had to settle for a 6-0 lead after two Laidlaw kicks.
Wallaby debutant Mike Harris got a penalty back for the home side before half-time, and then tied things up immediately after the break.
And with the momentum seemingly swinging towards the home side it took some sensational defence to keep the Scottish line unbreached.
Rob Simmons thought he had got the first try when he went over just before the hour mark but after consultation with the TMO Australia had to settle for a five-metre scrum.
Robbie Deans’ side continued to pile on the pressure, and finished with more than two thirds of both possession and territory but a backs-to-the-wall effort from the Scots kept them out.
And with time nearly up Scotland produced a huge effort on a scrum deep in Australian territory, and when the Wallaby scrum collapsed, Laidlaw made no mistake.
The result sets Scotland up perfectly for the remainder of their summer tour, where they will face Samoa and Fiji, and Grand Slam champions Wales will also be desperate to rub salt into the wounds of the Australians in their three-Test series starting on Saturday.