Australia went to lunch on Sunday at 3-157 and with a lead of 167, after Filer claimed the vital wickets of Ellyse Perry and Tahlia McGrath in the space of two overs.
Beth Mooney remains at the crease for Australia on 73, with the Queenslander holding the power to bat England out of the match in the final two sessions of day four.
But after Filer’s spell, there is hope for England.
After claiming Perry’s scalp for 99 in the first innings, the right-arm quick angled a ball in at the Australian superstar and had her dismissed, playing-on, for 25.
She then sent one through Tahlia McGrath when she seamed the ball back into the South Australian, giving England genuine hope with a fifth day in play for this Test match.
The 22-year-old Filer was chosen to make her international debut in the Test after impressing selectors with her speed following slight technical changes during the English winter.
Filer has regularly been able to get the ball up around the helmet of Australia’s batters, on a wicket offering little carry or bounce for other bowlers.
Earlier, Phoebe Litchfield was dismissed leaving a ball for the second time in her debut match, bowled by Kate Cross when she seamed a ball back into the left-hander from around the wicket with the opener on 46.
With Mooney unbeaten though, Australia would still believe they have a chance to bat England into submission.
The highest successful chase in a women’s Test remains Australia’s 3-198 in 2011 against England, while the highest score in any fourth-innings is England’s 9-245 in Canberra last year.
The best batter in the women’s game in recent years, Mooney set the tone for the morning when she hit back-to-back boundaries off Kate Cross through the off side.
England had a golden chance to remove her, when she hit a ball back at bowler Nat Sciver-Brunt on 55, only for the veteran to put her down in her follow-through.
The result of the Test looms as crucial to the outcome of the multi-format Ashes, with four points available for the Test before two points are up for grabs in each of the three ODIs and T20s.