England went to lunch on Saturday at 3-308 in reply to Australia’s 473 with Beaumont quickly whittling away the tourists’ lead after moving to an unbeaten 144.
Nat Sciver-Brunt was the only Englishwoman to fall in the morning session, out for 78 when caught behind trying to cut an Ashleigh Gardner delivery.
But otherwise it was all England in the opening two hours, with Sciver-Brunt and Beaumont combining for a 137-run third-wicket stand to put Australia on the back foot.
The pair were patient throughout the third morning, capitalising when Australia’s seamers got their lines wrong.
Australia again also offered England some lives.
After Beaumont survived several chances on Friday, Sciver-Brunt offered another on 42 early on Saturday when she slashed a Kim Garth delivery through the slips.
Sciver-Brunt also appeared to be dismissed on the first ball of the day when given out lbw to Darcie Brown, before ball-tracking showed it missing leg stump on review.
She struck three boundaries in row off Annabel Sutherland early in the day, hitting her through the legside twice and then guiding a ball behind point to the boundary.
The 30-year-old looked on for her second Test century, before Gardner speared a ball in and cramped the right-hander for room as she tried to play a cut shot.
It was Gardner’s second wicket of the innings, after also removing Heather Knight caught behind on 57 on Friday evening in figures of 2-61.
Still, England’s batters have put them on course to record the highest score against Australia in a Test, with that figure standing at 414.
They have also given them every chance to take control of the Test, which is the first women’s fixture to be played over five days in more than 30 years.
The Test match is worth four points in the multi-format Ashes series, with the three ensuing ODIs and three T20 matches all worth two each.