Low single-digit temperatures greeted the field for the first of two half-hour practice sessions at the Launceston circuit.
Most of the early movement came on the very first runs, Cam Waters bursting out of the blocks with a 51.257s.
That time would remain as the benchmark until much later in the session as the field settled into longer runs.
As usual the turn 4 hairpin proved problematic for a number of drivers, Kostecki the first to overshoot the braking marker and need to make a three-point turn.
The likes of Andre Heimgartner, Scott Pye and Bryce Fullwood would later do the same.
It wasn’t until the final minute that the Waters time was bettered as a number of drivers switched to green tyres.
The best of the late improver was Kostecki who jumped more than a tenth clear of the field with a 51.014s.
“I learnt how to find reverse in the session,” joked the Erebus driver. “The car feels pretty balanced. I’m not sure how many guys ran greens, but it’s a good start to the [weekend] here in Tassie.”
James Courtney ended up second fastest with a 51.163s while Todd Hazelwood made up 18 spots on his final lap to end up third.
Will Davison jumped Waters on his final lap, while Waters, who didn’t improve on that early time, was shuffled back to fifth.
Will Brown was sixth fastest in his Erebus Camaro ahead of Shane van Gisbergen and Mark Winterbottom.
Jack Smith was ninth for Brad Jones Racing with Broc Feeney 10th.
Practice continues with the second 30-minute session at 10:55am local time.
Tasmania SuperSprint practice 1 results