The Erebus driver put his Coca-Cola Camaro on top early in the third of three 45-minute sessions with a 1m11.616s.
That time stood for half an hour until Tim Slade kicked off the qualifying simulations by jumping to the top with a 1m11.564s.
Several minutes later Shane van Gisbergen went for a green tyre run, complaining of a gearbox issue on his first lap before he went quickest with a 1m11.462s on his second.
Kostecki then jumped back on a green tyre for a final run, during which he was able to pip van Gisbergen by 0.05s.
Cam Waters was the last driver standing to try and shade Kostecki, the Tickford driver going purple in the first sector before losing time over the rest of the lap and ultimately not improving.
That sealed bragging rights for Kostecki and Erebus ahead of the first Gen3 qualifying session tomorrow.
"It's great to roll out here with some speed," said Kostecki.
"I was really focussed on race runs in the first practice and second practice and I felt like a bit of a wobbler. She's a bit of a handful on old tyres.
"We're trying to be as prepared as much as possible with these new cars and it's starting to pay off. It's only Friday but I'm really excited about tomorrow."
Chaz Mostert slotted in between van Gisbergen and Slade in the closing stages of the session while James Golding ended up right behind his PremiAir Racing teammate.
Nick Percat capped off a promising day for Walkinshaw Andretti United with the sixth quickest time ahead of Will Davison, Scott Put, Waters and Anton De Pasquale.
Will Brown, meanwhile, earned the unwanted tag of being the first driver to nose a Gen3 car into the wall.
The Erebus driver lost the rear into Turn 8 and went straight into the tyres barrier, although was able to back out and continue without any serious damage.
He went on to finish the session 12th fastest.
The field spread was remarkably close across the 25 cars, 24 of which were within a second, while Jack Smith was 1.2s off in 25th.
Qualifying for Race 1 kicks off at 11:15am local time tomorrow.
