Australia captain Stirling Mortlock returns to outside centre after recovering from a shoulder injury which kept him out of the pool victories over Fiji and Canada.
Rookie fly-half Berrick Barnes and scrum-half George Gregan return to the side after being rested for the Canada game.
Connolly said the need to play a "slightly tighter game" prompted the selection of the versatile Ashley-Cooper, who starred on the wing.
But he said: "It was a points decision. Adam did very well in the All Blacks game (scoring a try in Australia's win). Drew has also done very well this tournament."
Connolly insists England are one of the Wallabies' major World Cup threats and told his side they must improve for Saturday's Marseille showdown.
"England are a very dangerous team. Their set-piece has been their cornerstone for many years and they have incredible speed out wide and a number 10 (Jonny Wilkinson) who steers them around exceptionally well," he said.
"When you look at our results through the pool games you would have to say we're pretty happy with where we're at.
"But we're very conscious that we have to improve considerably on that to go any further in the tournament."
Australia team to play England in the World Cup quarter-final in Marseille on Saturday: C Latham; A Ashley-Cooper, S Mortlock (capt), M Giteau, L Tuqiri; B Barnes, G Gregan; M Dunning, S Moore, G Shepherdson, N Sharpe, D Vickerman, R Elsom, G Smith, W Palu.
Replacements: A Freier, A Baxter, H McMeniman, S Hoiles, P Waugh, J Huxley, D Mitchell.