Knight smashed an impressive 157 and Marsh hit a belligerent 55 from 304 deliveries as the hosts made 314 all out.
That was just 17 runs shy of Australia's declared first-innings total of 331 for six - a target that looked a long way off when England were wobbling on 113 for six at one point on day two.
At the start of their second innings, Australia reached 64 for one at stumps for an overall lead of 81 runs heading into the final day, when only a glut of early wickets or a generous declaration is likely to force a result.
Knight and Marsh combined for a record seventh-wicket partnership of 156 after coming together with England 218 runs in arrears, the pair surpassing England's previous best of 110.
Knight made her century in the first hour of Tuesday morning after 263 balls and 11 boundaries, while Marsh held firm for almost six hours at the crease and took 225 balls to hit the first four of her watchful innings.
Unsurprisingly, Marsh's 330-minute half-century was the slowest for England Women in Tests.
Their partnership was broken shortly after Knight passed 150 with a four through extra-cover, the opener run out after setting off for an ambitious single and being sent back by Marsh.
Marsh was bowled by Megan Schutt shortly after completing a laborious half-century, after which the England tail conceded meekly.
There was still time for Australia to start their second innings either side of a late rain shower, with Rachael Haynes their sole casualty after being removed by Jenny Gunn for 23.
Marsh was happy with the role she played, however, and said afterwards: "I think when I went in we were pretty up against it. I was just really pleased to be able to hang in there with Heather and support her.
"It was the job the team needed and I tried to stick in there and be disciplined with my decision-making. It was really helpful to have Heather at the other end for the vast amount of the time I was there because she just played brilliantly and we kept each other going."