Healy, back leading the team after not playing in the recent T20 series, laid the foundation in the run chase with 50 off 70 deliveries.
She had great support from aggressive opening partner Phoebe Litchfield (32) before combining with run machine and player of the match Mooney (76 off 79) as Australia chased down India's 214 all out in 38.2 overs.
Mooney brought up 3000 runs in ODI cricket and became the fourth Australian woman to 7000 international runs, joining Meg Lanning, Ellyse Perry and Healy on the prestigious list.
The 32-year-old lofted two brilliant sixes down the ground in an innings of class and great tempo.
She had a wonderful ally at the end of the run chase in Annabel Sutherland (48no off 44) in an 85-run stand for the fourth wicket.
Australia and India are now on four competition points each in the multi-format series after India won the T20 series 2-1.
Australia's bowlers shone to restrict India after the hosts suffered injury blows before their team could be named.
Stars Ellyse Perry and Kim Garth were ruled out of the series before India won the toss and elected to bat at Brisbane's Allan Border Field.
Both suffered quad strains in the T20 loss to India on Saturday.
Fast bowler Megan Schutt, not originally in the squad, was called up and took a wicket with the second ball of the innings when she trapped Pratika Rawal in front for a duck.
At the other end Darcie Brown took an athletic caught-and-bowled to dismiss Shafali Verma (four) and put the visitors on the back foot early.
The spin of Ashleigh Gardner, Alana King and Sophie Molineux kept the pressure on, with the trio claiming wickets in the middle overs to keep the run rate down.
Gardner (3-33) had the best figures but all seven bowlers used by Australia did their jobs.
Medium-pacer Tahlia McGrath claimed the key scalp of in-form opener Smriti Mandhana (58 off 68 deliveries) when she swept an innocuous leg-side delivery to deep fine leg.
India skipper Harmanpreet Kaur (53) and big-hitting allrounder Kashvee Gautam (43) rescued the innings when it was looking rocky.
The fielding of Georgia Voll - who took three catches - was a highlight, especially her brilliant diving effort to dismiss Kaur.
Gardner finished the India innings in the 49th over when her slick flick at the stumps ran out the dangerous Gautam.
Earlier, Cricket Australia released a statement about Perry and Garth's likely return ahead of the one-off Test at the end of the ODI series.
"Their availability for the Test match will be further assessed at the end of the ODI series pending on how they progress with rehab," the statement said.
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