The two contenders, who came into the weekend first and second in the standings, were hit early in the race, both Kostecki and Mostert caught up in adjacent, but seperate, incidents.
Kostecki had made a strong start, working his way up to second behind teammate Brown by the third lap.
However his race unravelled at the hairpin on that lap when he was initially nudged from behind by Jack Le Brocq before side contact with Cam Waters, who was trying to sneak into second.
The Waters contact broke the front-left steering arm on Kostecki's car, forcing him into the pits for five laps.
Seconds later Mostert ended up facing the wrong way after being tipped into a spin by Broc Feeney.
That left Mostert with a broken steering rack, out of the race and unimpressed with Feeney – particularly when the incident was cleared by race control.
"It's very early on in the race and some young guys are a little bit keen to try and get their nose maybe where its not supposed [to be]," he told the Fox Sports broadcast. "Im pretty disappointed to see no further action [from race control] because I'm out of the race."
Out front Brown continued to lead the field, while the early drama was great news for the likes of Waters, Andre Heimgartner and Shane van Gisbergen who filtered up to second, third and fourth.
Waters and Heimgartner were the first of that lead group to pit on lap 21, Heimgartner jumping Waters in the process.
Brown then followed suit a lap later, resuming ahead of Heimgartner and Waters while van Gisbergen took over the lead of the race.
The reigning champion went four laps longer before taking his mandatory service, slotting back into what was effectively fourth place.
The leaders then settled into a rhythm for the second stint, Brown leading Heimgartner by just under a second, Waters drifting back and van Gisbergen recovering from being undercut on his fresher rubber.
As the race wore on it became two seperate battles, Brown and Heimgartner left to duke it out for the win.
But while Heimgartner proved stubborn he couldn't quite get close enough to Brown, the Erebus driver winning by six-tenths.
"Andre was hustling at the end; I could see he was catching me a bit, I was just trying to save my rear tyres," Brown explained. "It was definitely squirming around a bit at the end.
"I knew once I got off the line [at the start] and saw the guys fighting behind me, that's what I needed to get into the lead and stay out there and watch for the undercut.
"Overall, I'm just ecstatic."
The battle for third was a thriller, van Gisbergen running down Waters with his superior tyre condition.
He got to the back of Waters on the very last lap, before getting under the Monster Mustang at the hairpin to set up a run down the back straight.
Van Gisbergen was then able to run Waters wide at turn 6 to nab third place.
Waters finished fourth, the only Mustang in the top eight, ahead of Scott Pye, Tim Slade, Le Brocq and Cam Hill.
Nick Percat had a strong race to finish ninth after starting 13th while Thomas Randle came from even further back to finish 10th.
Kostecki, meanwhile, was forced to make another late stop with his wounded Camaro and was ultimately classified 23rd.
He was able to retain the series lead, although his margin was cut from 100 points to 74 points.
Mostert's DNF was more costly, the Walkinshaw driver dropping from second to fourth in the standings behind van Gisbergen and Brown.
The Tasmania SuperSprint continues with two qualifying sessions and two more races tomorrow.
