Gardner's attacking offspin returned Australia's best figures of the innings - 4 for 99 in 25.2 overs - and, with two days of the Test remaining and an overnight lead of 92 thanks to an ominously composed opening stand of 82 between Phoebe Litchfield and Beth Mooney, she's confident of having an even greater say in the fourth-innings endgame.
"We've got a lot of bowling options, we've got three spinners," Gardner said at the close. "So when I get the opportunity, I want to make sure that I use it. We've never played a five-day Test match, so knowing that that wicket will deteriorate at some point, spin is going to play a huge role for the rest of the game. I would certainly say there's going to be a result, and that's what we're going to be pushing for."
Both teams are about to enter into the unknown, given that previous women's Tests have been contested across four days and therefore this sort of match situation would previously have been a nailed-on draw - much like England's last five Tests since 2015.
Instead, the contest is set to be a battle of stamina as much as skill - a point that Beaumont acknowledged at the close, after sensing that even Australia's multi-faceted attack had been short of ideas for long tracts of her innings, not least when she and Danni Wyatt were stepping up the tempo in a lively afternoon stand of 72 that spanned 18 overs.
"It certainly ebbed and flowed all day, but most of the time I feel they were a bit flat," Beaumont told Sky Sports at the close. "But that's Test cricket. On a hot day, and when you're batting well and there's not a lot in the pitch, it is difficult, so fair play to them, really.
"I don't think they expected us to play the way we did and take it to them, and get as close as we did," Beaumont added, after England conceded a mere ten-run deficit in their first-innings 463. "The key moment was myself and Danny Wyatt's partnership. I feel like that was where we really could have stretched them, and taken the game away from them."
Gardner, however, believed that her own team's struggle for breakthroughs augured well for their second innings, given that it will be England facing the tough challenge of batting last.
"Tammy batted really well, pretty much any bad ball that was missing the stumps, she put it away to the boundary," Gardner said. "I guess that shows, from a batting point of view, that whenever they do miss the stumps, there's almost a free shot out there. On the flip side, when we've got the ball in hand again, we've got to make sure that we really hone in on the stumps and just be really relentless.
"We don't necessarily want to draw a Test match. And we're certainly in a pretty good position to push the case forward, but we just need to think small, and not think about the endgame," she added. "We just need to work in small periods of the game, and get ourselves into a really good position to hopefully go out there and try and win it."
The speed of Litchfield's and Mooney's progress in Australia's second innings rather confirmed the impression that they'd absorbed those lessons from England's innings, as they rattled along to the close at 4.31 runs per over. And though Lauren Filer's extra pace caused a couple of deliveries to skid through low to Litchfield in particular, that prospect could be something of a double-edged sword for England come day five.
"We've just got to be patient, keep the sticks in play, and if it stops swinging, maybe go to that cross-seam," Beaumont said. "It's a really big morning session, I reckon. If we can get a few wickets, we can get on a roll and you're seeing now that the wickets are starting to come a bit in clusters. It's quite hard to start on this surface so you've just got to stay positive.
"Nobody came here for a draw so, if they set us a target, I have a feeling that we'll be giving it a good old crack," she added. "We'll have to wait and see what the Australians do. You'd hope that they'd want to be pushing for a result and set something up, but you never know really. It's so early on in the Ashes and every single day, it's been like, the team doesn't want to crack first."
Gardner, for her part, said she had no idea yet what an appropriate fourth-innings target would look like, but said her side would be focussing on "ten-over blocks" as they look to capitalise on "any bad bowling that [England] do dish up".
"That's super-important when you're going into day five of a Test match, which we don't normally do," she said. "There's still so much time in the game. There's still 180 overs to go, so we're not used to that, but it's an exciting prospect."
Andrew Miller is UK editor of ESPNcricinfo. @miller_cricket