Resuming the day at 143 for three, Ellyse Perry (68 not out) and Ashleigh Gardner (51) went on to share an 89-run stand before Indian pacers triggered the batting collapse, reducing Australia to 240 for nine from 208 for four.
In what seems as an attempt to move the game forward, Meg Lanning declared the innings before her team could be bowled out.
India ended with a 136-run lead.
After Deepti Sharma got rid of Gardner, debutant Meghna Singh once again troubled the batters with her outswingers as India took four wickets after the new ball was taken in the 81st over.
Pooja Vastrakar and Jhulan Goswami were also on target.
With close to 70 overs left in the game, draw still looks the most probably outcome after substantial time was lost due to rain on the first two days.
Perry, who averages more than 78 in Test cricket, could have been out as many as three times but had the luck on her side. While one was a close LBW shout, she was also dropped twice.
Meghna took her maiden wicket with a beautiful outswinger to have Annabel Sutherland caught behind. Her second wicket was Sophie Molineux who was foxed by Meghan’s inswinger to the left-hander.
Pooja had Georgia Wareham caught behind before offie Deepti Sharma took her second wicket of the day with an arm ball to dismiss Darcie Brown.
Indian pacers have bowled better than their Australian counterparts and have been able to hit the corridor of uncertainty for the batters on a consistent basis.
India Women: 377 for 8 declared in 145 overs (Smriti Mandhana 127, Deepti Sharma 66; Sophie Molineux 2/45, Stella Campbell 2/47, Ellyse Perry 2/76)
Australia Women: 241 for 9 declared in 96.4 overs (Ellyse Perry 68, Jhulan Goswami 2/33, Pooja Vastrakar 3/49)