The Southern Stars claimed a 106-run first innings lead after dismissing England for 168 in Canterbury on Wednesday.
The visitors resumed at 8/268, with all-rounder Jess Jonassen (99) falling agonisingly short of a century in her Test debut, before the team declared at 9/274d.
Ellyse Perry (3/38) tore through England’s top-order, removing Lauren Winfield (1) and Sarah Taylor (0) in successive balls.
Megan Schutt bowled 11 maidens on her way to career-best figures of 4/26 from her 18.4 overs. Sarah Coyte (2/30) and Jess Jonassen (1/36) rounded out the Australian wicket takers.