India then returned to overhaul the target, scoring 177 for three in 19.4 overs.
Sixteen-year-old Shafali Verma finally came good, blasting a 28-ball 49 to give India a flying start. Her innings contained eight fours and a six.
Smriti Mandhana (55) also smashed seven boundaries in her 48-ball innings to anchor the tricky chase.
Jemimah Rodrigues also came out all cylinders blazing, making a quickfire 19-ball 30 with five fours.
In the end, skipper Harmanpreet (20 off 20 balls) and Deepti Sharma (11 off 4 balls) took the team home.
Earlier, Gardner sent the ball across the fence 11 times and blasted three sixes in her 57-ball innings to emerge as the top-scorer for Australia.
For India, Deepti Sharma (2/27) was the most outstanding bowler, snapping two wickets, while Rajeshwari Gayakwad (1/34), Radha Yadav (1/34) and Harleen Deol (1/21) took one wicket each.
Ellyse Perry (1/33), Megan Schutt (1/26) and Nicola Carey (1/27) accounted for one wicket each for Australia.
With this win, India moved to the second position in the points table, behind England.
India had lost to Australia and England by an identical four-wicket margin in their last two matches in the series.
Australia will take on England in the final league match of the series on Sunday.
Australia women: 173 for five in 20 overs (Ashleigh Gardner 93; Deepti Sharma 2/27).
India women: 177 for three in 19.4 overs (Smriti Mandhana 55, Shafali Verma 49; Megan Schutt 1/26).