Australia went to stumps on day one at 3-96 in reply to India's 198 on Friday at the revamped WACA Ground.
Healy entered the fray late on with Australia battling at 2-31 following the dismissals of openers Phoebe Litchfield (9) and Georgia Voll (2).
With the pink ball swinging wildly under lights and the WACA's new water slides pumping in the background, Healy endured a series of nervous moments in front of 3439 spectators before falling for 13 when she spooned a catch to backward point.
But star allrounders Ellyse Perry (43no) and Annabel Sutherland (20no) guided Australia to stumps, with the pair to front up again on Saturday on a day when the mercury is forecast to hit 39C in Perth.
Sutherland was the star of the show on day one, snaring a career-best 4-46 off 17 overs and watching four other catches go down off her bowling in a butter-fingered effort from Australia.
Teenage debutant Lucy Hamilton (3-31 off 11) was also excellent on a day when the temperature hit 36C.
Hamilton snared the first wicket when she bowled star opener Smriti Mandhana for four in the sixth over, sparking wild celebrations.
"Smriti is a really high quality player, and it was nice to get my first wicket," Hamilton said.
"Obviously in the ODI I didn't get a wicket, so it was nice to get that and kind of get the monkey off the back.
"And then it kind of just kept rolling on from there."
Wickets fell at regular intervals after Hamilton's initial strike, but Australia's grassed chances proved costly.
Sutherland had four catches dropped off her bowling.
The first came when Hamilton grassed Indian debutant Pratika Rawal at gully.
Rawal, who was four at the time, went on to make 18.
Captain Harmanpreet Kaur, who was dropped at gully on 10, went on to make 19, but the most costly missed chance was when Jemimah Rodrigues played a shot to Voll at short leg.
Voll couldn't hold the one-handed chance when Rodrigues was yet to score.
The India batter went on to make 52 off 84 balls, with her knock including four consecutive boundaries from leg-spinner Alana King's first over of the day in the 40th over.
Hamilton eventually had Rodrigues caught at square leg, but her half-century ensured there was no dire crumble from India.
Sutherland watched a fourth catch off her bowling go down when wicketkeeper Beth Mooney had three juggles before dropping an easy edge from Kashvee Gautam.
Gautam was on 16 at the time, and she went on to make an unbeaten 34 off 54 balls.
India unleashed three debutant pace bowlers for the match, and it was Sayali Satghare (2-24) who struck first with a wildly swinging delivery that started well outside off before crashing into the top of Voll's leg stump.
Litchfield departed a short time later when Rodrigues took an excellent diving catch at backward point.
But it was Healy's dismissal that was the most deflating, with the retiring 35-year-old left to rue her decision to reach for Satghare's wider and slower delivery.
Healy may still have one more chance to bat, especially if Australia are unable to manufacture a huge first-innings total.
Australia lead the multi-format series eight points to four, meaning India must win the Test to come away with a draw.