The half-hour session was mostly a quiet affair, an early 1m06.049s from David Reynolds setting the pace until the final few minutes.
That was when a handful of drivers ventured on new rubber, Brown jumping to the top with a 1m05.970s.
At that same point James Courtney slipped into second with a 1m06.018s, before Mostert jumped them both with a 1m05.935s to claim top spot.
"The car felt pretty good," said Mostert. "We've still got some things we need to work on.
"It's a pretty tricky session for us; the Porsche rubber goes down and the cars really light up at the start of the session. It was nice to go a little bit quicker towards the end there but we had to use a new set of tyres to do that.
"Who knows where anyone is in practice, we'll keep working on ourselves."
Brown and Courtney were second and third while that early lap from Reynolds was good enough to hang on to fourth place.
Andre Heimgartner was fifth fastest for Brad Jones Racing ahead of Cam Waters, while Nick Percat had a promising run to seventh after tough outings in Perth and at Winton recently.
Mark Winterbottom, Jake Kostecki and Thomas Randle rounded out the Top 10.
There were plenty of big names missing from the pointy end of the field as the likes of Triple Eight and Dick Johnson Racing focussed on race set-up.
Will Davison was best of the drivers from those teams in 14th while Anton De Pasquale was 16th, Shane van Gisbergen 17th and Broc Feeney 22nd.
Hometown hero Bryce Fullwood had a tough start to the weekend, the Darwin local going off at the end of the session and tagging the wall on the outside of Turn 11. He ended up 27th and last.
