Forced to pursue 330 for an unprecedented triumph, opener Healy led superlatively from the front with 142, her sixth ODI hundred, her first as captain and the biggest innings of the tournament as Australia edged home by three wickets in a Sunday special.
When it came down to a nervy denouement, Healy's evergreen pal Perry, who'd earlier had to retire with cramp, re-emerged and proved the rock in the penultimate over, hitting the straight driven six from Sneh Rana to take the champions to 7-331 and seal a classic victory with six balls remaining.
Perry, the cool finisher on 47no, was given sterling help at the death by fast bowler Kim Garth, who had also hit a reverse sweep for four in that key 49th over from Rana as the Aussies knocked off the 13 they needed.
"Great result. To chase down 330 in 50-overs game is new territory for us -- hopefully don't have to do it again," beamed the weary Healy.
"Really proud of the group. It got a little bit tight, but we have been preaching about the depth in our line-up, and the fact we could chase this proved it."
Earlier, Healy, who'd put India in to bat in front of a packed house, felt Annabel Sutherland's five-wicket haul was critical to checking India's formidable charge, with Smriti Mandhana again starring for the rampant hosts.
The world's No.1 ODI batter Mandhana struck her fifth successive 50-plus score against Australia this year, her dazzling 80 off 66 balls strongly supported by youngster Pratika Rawal (75 off 96) as the openers put on 155 befor halfway.
"Eight overs in, I was like 'what have I done?'," sighed Healy. "I thought we were going to be chasing 380 at one point, but the bowlers pulled it back."
Particularly Sutherland, whose 5-40 was key as India lost their last six wickets for 36.
Slow left-armer Sophie Molineux also made a good comeback, getting three wickets, including Mandhana's, despite going for an Australian World Cup worst of 75 runs off her 10 overs..
Useful contributions from Harleen Deol (38 off 42), Jemimah Rodrigues (33 off 21) and Richa Ghosh (32 off 22) still put the utmost pressure on the champions.
But 35-year-old Healy rediscovered her devastating, pugnacious best from the start, racing to her hundred off 84 balls and going on to 142 off 107, featuring 21 fours and three sixes.
"To contribute heavily was great. Would have liked to stay a bit longer but the girls got the job done," smiled Healy, who hadn't scored an ODI ton for over three years.
Australia were boosted by opener Phoebe Litchfield (40 off 39), with whom Healy put on 85 in just 11.2 overs, Perry, who'd had to retire while cramping when she'd got to 32 only to return five wickets later after the sixth had fallen, and Ash Gardner, who made 45 off 46.
The victory put Australia back on top of the league table, still unbeaten after four matches, with three wins and a wash-out, and now well on course to the semi-finals after their 12th straight completed World Cup match win stretching back to 2022.
For India, though, the pressure is on after they lost their second match in four days, following the shock defeat by South Africa.
At least they could celebrate Mandhana, who's scored three centuries this year against the Aussies, and became the first woman batter to make 1000 ODI runs in a calendar year.
When she smashed Kim Garth over extra-cover for six, it also brought up her 5000 ODI runs. She's the youngest - and quickest - player to the landmark.
