Kostecki was compelled to recuperate after a sluggish begin from pole place, overhauling each Chaz Mostert and Thomas Randle within the first stint.
He then benefited from a fierce battle between the pair behind him, ultimately cruising to a 1.7s win.
His collection lead is now 80 factors over Shane van Gisbergen, with Broc Feeney in third, 99 factors behind.
Brown’s title hopes took successful, in the meantime, because the Erebus driver taken out of the race in a first-lap crash. He’s now fourth within the standings, 141 factors behind his team-mate.
The conflict was triggered by Jack Le Brocq drilling Brown on the best way by way of Flip 1, after Brown had checked up from gentle contact with Anton De Pasquale.
Brown’s entrance bar went flying within the melee that adopted, whereas Cameron Hill was compelled to spin his MSR Camaro to keep away from the mess and was subsequently collected at velocity by Jack Smith.
The incident put Brown, Hill and Smith out of the race on the spot.
On the entrance of the sphere, Randle made a fast begin from exterior the entrance row to take an early lead. Mostert’s begin from fifth was even higher, as he slipped into second forward of polesitter Kostecki.
The crash led to a four-lap security automobile, and on the restart, Randle continued to steer the sphere, initially forward of Mostert. That was till Kostecki pulled a daring transfer on Mostert at Flip 6 on lap eight to nab second place.
By lap 11, Kostecki was onerous on Randle’s bumper, taking a look across the exterior of Flip 6. He then acquired the job accomplished later within the lap, with Randle and Mostert each diving instantly into the pits.
They resumed nose-to-tail in the identical order, squabbling over place from the second they left the lane.
Kostecki charged on earlier than stopping two laps later, the battle between Randle and Mostert holding them up simply sufficient for Kostecki to renew within the lead.
His trigger was additional helped on his out-lap when Mostert dive-bombed Randle into Flip 6, with the pair making contact on the exit, which ran Randle huge as Mostert moved into second.
The trade gave Kostecki the respiration room he wanted to determine a lead that he would maintain till the chequered flag.
“I made it a bit onerous for myself, I did not get a superb leap initially,” stated Kostecki. “Chaz and Tom each acquired a superb begin so I needed to move them again earlier than the cease. Fortunately this Camaro had loads of tempo below its bonnet.
“It is necessary to maintain on constructing that [points] buffer. The workforce executed flawlessly and its days like in the present day that you’re going to cherish eternally.”
Mostert got here residence second, whereas Randle got here below strain from team-mate Cam Waters within the closing phases of the race.
Waters was ultimately advised to not battle Randle, but it surely did not cease him closing proper up on Randle’s bumper as they crossed the road third and fourth.
That marked each a career-first podium and greatest end for Randle.
Van Gisbergen ran down Triple Eight team-mate Broc Feeney within the second stint, with Feeney having stopped on the primary inexperienced flag lap after the security automobile.
The Kiwi then did his common trick, ran lengthy and had higher tyre situation to get previous his team-mate within the closing phases.
Feeney completed sixth forward of Ford trio Matt Payne, James Courtney and Will Davison, with Andre Heimgartner in tenth.
The occasion continues with two qualifying classes and two extra races on Sunday.