Kostecki ran last in the single-lap dash for pole thanks to topping qualifying on Friday afternoon.
To that point Broc Feeney was fastest, Kostecki chasing a 2m04.755s to secure pole for the 2023 running of the Great Race.
He made a ropey start to his lap, dropping his right-rear tyre off the back of the exit kerb at the first corner.
That left him trailing Feeney by just under a tenth at the first sector, but, after a big push over the top of the Mountain, he found himself more than three-tenths up at the second sector.
From there it was a case of keeping it clean in the final sector, Kostecki's final margin for pole the best part of half a second.
"It means a lot to the whole team," said Kostecki.
"We've been so fast all weekend and I thought I threw it all away at turn 1 there. I have a delta on my dash and I knew I had a bit of time to make up.
"The car was awesome across the top and I just threw it down the hill. I wasn't sure if I was going to come out the other side. I was very happy to get through the dipper and I knew going down Conrod I was on a good lap and just needed to not stuff it up. I'm very proud of this whole team."
Feeney made up three spots on regular qualifying to end up on the outside of the front row, while Cam Waters made up one spot to qualify third, best of the Ford Mustangs in the field.
James Golding lost two spots compared to qualifying, but still ended up a highly-credible fourth in his first Bathurst 1000 Shootout.
Anton De Pasquale and Shane van Gisbergen were fifth and sixth fastest respectively, while David Reynolds pipped Grove Racing teammate Matt Payne for seventh.
Chaz Mostert matched his qualifying effort with ninth in the Shootout, while Will Davison stayed in 10th after making small mistakes at Hell Corner and McPhillamy.
