Australia won the previous meeting against the Scots 21-15 at Murrayfield in 2013 to snap a two-match losing streak against the ninth-ranked nation on the IRB standings.
Giteau's off day with the boot contributed heavily to Australia's 9-8 loss to Scotland at Murrayfield in 2009, while the Wallabies suffered another embarrassing 9-6 loss in cyclonic conditions in Newcastle in 2012.
Scotland scraped into the last eight with a 36-33 win over Samoa to finish second in Pool B but Giteau is expecting a tough battle against Vern Cotter's side.
"They've been very impressive," Giteau said.
"Their set-piece game looks very strong, obviously they've got a great goal kicker and captain (Greig Laidlaw) who leads them around really well.
"They look like a very confident team who know what they want, and know the style of rugby they want to play, and they've been executing it very well."
The Wallabies are coming off impressive wins over England and Wales which saw them finish top of Pool B, but skipper Stephen Moore is also wary of the Scots.
Australia have only met Scotland once before at a World Cup – in 2003 – when they recorded a 33-16 win in the last eight, but the recent losses have Moore on high alert ahead of this weekend's clash.
"It shows you how difficult the task is," Moore said.
"They're a quality team, who've shown that in the tournament so far.
"Certainly, every time I've played against Scotland, I've felt it's been a really tough test match.
"These games are really tight and it's the small margins that are going to be important so that's important that we prepare that way."