The second half-century partnership in a row between Harmanpreet (54) and allrounder Kashvee Gautam (25) gave India a total to defend, although it was short of the 270-plus score the pitch suggested was a par tally.
Annabel Sutherland took 2-37 and Australia's spinners Ashleigh Gardner (2-39) and Alana King (2-41) did well to restrict India, who will rue not making the most of several dropped catches after winning the toss.
Australia suffered another injury blow ahead of the match with spinner and vice-captain Sophie Molineux sustaining a back injury.
Molineux's place in the side was taken by allrounder Nicola Carey, in her first ODI since 2022.
India progressed to 78 without loss before Australia got back in the contest.
In-form Smriti Mandhana (31) was bowled by Gardner while playing a paddle sweep after a streaky knock.
Mandhana was dropped on 15 by Gardner, a tough chance that she dived for one-handed to her left at point.
Tahlia McGrath made a meal of another chance running back from mid on when Mandhana was on 26.
At the other end Pratika Rawal (52) was in serene form with her cover drives all class.
She threw it away when calling for an ill-advised single to mid-on. Harmanpreet turned her back and Rawal was stranded.
Deepti Sharma made just one before a swipe to deep midwicket off King brought about her demise.
Beth Mooney took a slick juggling catch to dismiss Amanjot Kaur, standing up to Carey, but missed a leg side stumping to dismiss wicketkeeper Richa Ghosh when she was on six.
Ghosh (21) was looking dangerous until King trapped her in front and it was 6-162
King should have had Gautam but Megan Schutt dropped a sitter in the deep.
Gautam and Harmanpreet both then settled into a crucial stand.
Cricket Australia earlier confirmed Molineux's injury in a statement on match day as India won the toss and elected to bat.
"Sophie Molineux has experienced some lower back pain and will not be available for the remainder of the series.
"She will continue to be monitored ahead of the upcoming tour to the West Indies."
Molineux, if fit, will captain the side in the Caribbean in mid-March with current skipper Alyssa Healy set to retire at the end of this series.
The multi-format series is level with both sides on four points after two wins a piece.
Australia won the opening ODI in Brisbane on Tuesday by six wickets after India prevailed 2-1 in the T20 segment.
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