The tourists were making good progress as Heather Knight produced a career-best score of 168 not out to take England within 40 runs of their opponents.
Katherine Brunt did further damage with the ball as she took two early wickets to leave the Aussies on 12/2 heading into the final day.
Rainfall prevented England from making further headway and that could leave them with too much to do with just one day to go in Canberra.
England captain Knight said: "(The rain was) really frustrating. We put ourselves in a really good position and the way we came out before lunch was exactly what I asked of them.
"Brunty's having a brilliant Test and the way she bowled - the aggression, the skill - hunting Australian wickets, and to pick up those two wickets felt like we could really break the game open, try and get them out for a cheap score and set up a chase, so obviously (it's) a little bit frustrating.
"We are still holding out a little bit of hope, there's a little bit of time left in the game so we are going to have bowl absolutely out of our skins to try and take early wickets and put the Aussies under the pump. We live in hope.
"We are focused on our plan, we are going to hit them hard in the morning, a 9.30am start might give us a little bit more with a bit of dew around. If we can skittle them it will set up a nice chase for us hopefully."
Looking back at her own career-best battling performance, Knights added: "I think it's my best innings for England, definitely.
"The situation we were in, in an Ashes game against probably the best team in the world - I'm super pleased.
"I felt quite rusty at the start, they bowled pretty well with the first new ball, but when you've played a lot of white-ball cricket and you have a red-ball moving it's quite hard not to have a little flirt with it and I did that a few times, but managed to get through that tricky period and when the spin came on I felt a lot more comfortable and found my rhythm."