The Erebus driver was untouchable across the session, securing provisional pole by over a tenth of a second with a rapid 2m04.664s.
That means he'll run last in the Top 10 Shootout on Saturday evening, which will determine the first five rows of the grid.
It was a different story for Kostecki's closest title rival Shane van Gisbergen, who only rescued his Shootout hopes with the seventh fastest time on his very last lap.
Brown, meanwhile, missed the Shootout altogether after a difficult session that started with a trip into the Turn 2 tyre wall.
Brown was responsible for a dramatic start to the 40-minute session, the title contender firing his Erebus Camaro into the wall on his first run.
That prompted an early red flag, Brown able to get the damaged car out of the tyre barrier and back to the pits to begin repairs.
After a little under 10 minutes the session went green again without a single representative time on the board.
And nobody could get a lap in before the red flag was back out, this time thanks to Fraser clouting the wall hard at The Cutting, putting him out on the spot.
The second stoppage was a blessing for Brown, giving his crew time to repair his car and send it back out just a few minutes after the next restart.
When the times did start to land they were spectacular, Cam Waters becoming the first driver into the 2m04s in a Gen3 car when he jumped to the top with a 2m04.990s.
Source: Autosport