The first of the back-to-back sessions started in wet conditions, giving drivers their first taste of the new softer Dunlop grooved tyre.
It was Kostecki go got the best out of the rubber and the conditions on his first run, leading teammate Will Brown by eight-tenths.
That proved to be critical as drivers failed to improve once moving to the hard compound slick tyre late in the session.
That wasn't just down to limited grip but also limited running, the session cut short when David Reynolds beached his Mustang at Turn 1.
That left the Erebus cars with a front-row lockout just a day after Kostecki scored his first Supercars race win.
"I knew that the new soft wet was quite fast and knew I was only going to get one lap out it, so we made sure we were pressured to get it right that first lap and just sent it," said Kostecki.
Bryce Fullwood put in an impressive first run to end up third on the grid for today's race ahead of Anton De Pasquale.
Matt Payne continued his strong debut at Albert Park with fifth on the grid from James Golding, Andre Heimgartner, Mark Winterbottom and Chaz Mostert.
Shane van Gisbergen, meanwhile, was left down in 11th after not getting his final run in due to the red flag, while Cam Waters was just 20th fastest in that session and Feeney a lowly 22nd.
The field switched to the super soft slick tyre for the second session to set the grid for Sunday's race.
The constantly evolving track conditions made for a hectic finish, pole not settled until the very last runs.
In the end it was Feeney that executed a perfect comeback after his underwhelming first session, the Triple Eight driver taking a first career pole thanks to a 1m47.768s.
"The highs and lows – 22nd and then first," said Feeney.
"I was pretty fired up between sessions. It's about time, I've been so close so many times.
"It's a credit to the team; the timing was perfect out there. I nearly stuck it in the fence not hat last lap there, crazy conditions."
Mostert was second fastest, just under two-tenths off pole, ahead of Brown, Heimgartner and Fullwood.
Jack Le Brocq was sixth fastest from Will Davison, Payne, Thomas Randle and Scott Pye.
Kostecki slipped back to 14th in the session second while it was another tough one for Waters who qualified 15th.
Reynolds' miserable morning continued in the second session when he ended up down the escape road at Turn 11 – and was subsequently collected by Brown.
Steering arm damage from the contact left him last on the grid.
Supercars returns to the track for the third race of the weekend at 5:30pm local time.
