A rebellious skirl of the bagpipes could be discerned within St James' Park on Saturday, in direct contravention of pre-tournament guidelines which prohibited their use within World Cup venues. But it really would be an act of revolt against the established order of things if Scotland could march to Twickenham next Sunday and ambush Australia.

Historically, quarter final ties at World Cups tend only to be the end of the road for Scotland, an unhappy date with one of the unforgiving juggernauts of the game. New Zealand (1987, 1995 and 1999), Australia in 2003 and Argentina in 2007 have all dismissed us at that stage, while only once, a home match with Western Samoa back in 1999, have Scotland been entitled to call themselves one of the top four teams on the planet.

Having already exceeded their 2011 effort, when they failed to exit the group stage, Vern Cotter and his side can already celebrate a successful tournament, but the Kiwi's next trick is to convince everyone that the impossible is in fact possible against one of the big hitters of the Southern hemisphere. This may not be no easy task, considering the four tries the Scots shipped against the Samoans. Last eight spot or not, you can still walk into a bookmakers shop and get odds of 150/1 against Scotland winning the thing.

The match is big enough without a portion of inter-Antipodean spice being added to the mixture. Quite aside from the Kiwi-Australian rivalry, Sean Maitland, the winger who was born in Tokoroa in New Zealand's North Island, is a first cousin, school friend and former team-mate of Australian fly half Quade Cooper. "He looked after me when we were six-year-olds," said Maitland. "It will be good to catch up."

"They're the form team at the moment as everyone has been saying," added the wing, who made his debut for Scotland at Twickenham, scoring a try in the process. "They obviously had a good win against England and they won ugly this weekend [against Wales] a bit like us. But it's knockout rugby and we're excited."

While the Aussies will deservedly be huge favourites, such odds are somewhat disrespectful considering some of the shock results which have taken place in this tournament. The Scots may even be in the rare position of gaining the support of any English-based 'neutrals' in the Twickenham crowd. "You've got to take your chances against these teams - South Africa, New Zealand, Australia - and the big northern hemisphere teams too," said Maitland. "I'm sure they will be looking at our game against Samoa and seeing some opportunities but we'll be looking at them as well. No team is perfect. I'm sure our defence coach and attack coach will be doing their homework and trying to devise a plan to beat Australia."

"It’s never job done," he added. "Vern has set high standards for this team. The boys have set high standards and goals. Scotland have had a decent record against Australia in the past. You’ve got to have that self-belief."

Centre Matt Scott revealed how the inspirational Cotter had sought to inspire his team in the locker room afterwards. "The message from Vern after the game was simply 'Believe in yourselves'," he said. "That’s a very un-Scottish trait, isn’t it? We don’t believe in ourselves. In every sport, we don’t believe that we’re up there with the best. But we must believe in ourselves. We absolutely must. If we give it 100 per cent next week and don’t get the result we want, fair enough. But we’re determined to give a good account of ourselves. We’re targeting a win next week, definitely."

Everything might not have gone exactly as the Scots had planned during the 36-33 win against the Pacific Islanders but at least, with no little assistance from captain Greig Laidlaw, they managed to regather themselves sufficiently to make sure that they found a way to win. The psychology, of course, will shift again for the quarter final against an Australian side who will be huge favourites. "It’s a horrible place, coming under the posts every five minutes," said Scott. "Greig was just saying: “Boys, don’t panic, don’t panic."

While late substitute Sean Lamont was mobbed in the changing room afterwards after racking up a century of caps, Richie Gray was simply delighted that his half century had a happy ending. "The reality of it is that if we got knocked out we were on the bus home and back at work on Monday," said the giant lock. "We are still in the biggest rugby tournament in the world and have a crack at the last eight. We have worked too hard for this. We are not going to let it slip. We will prepare well and have a right good crack at it. But we have to improve. If we try and put in a first half performance like that the game will be over."