The two Erebus drivers ran second last and last in the Shootout after topping qualifying, Kostecki ahead of Brown, earlier today.
Both drivers had to overcome early pacesetter Cam Waters in the single-lap dash for pole, who made up five spots compared to qualifying to lead the way with two cars to run.
Brown, running second last, through the gauntlet down to series leader Kostecki with a rapid 1m08.455s on his lap.
Kostecki did his best to respond but fell a tenth short, ensuring an Erebus front-row lockout but conceding pole to Brown and Perkins.
"I'm petty pumped about this one," said Brown.
"Enduro season is always awesome. To get pole at at the Sandown 500 is amazing. I knew I had a really fast teammate going out behind me and I had to out a good lap together. I'm stoked with it."
Waters ended up the best-placed Ford in third ahead of Dick Johnson Racing Mustang driver Will Davison, who made up three spots compared to qualifying.
Triple Eight driver Broc Feeney slipped from third in qualifying to fifth in the Shootout, while Todd Hazelwood slipped back one spot to end up what is still a credible sixth on the grid for Blanchard Racing Team.
The two Grove Racing cars were next, rookie Matt Payne edging veteran David Reynolds for seventh.
Thomas Randle lost five spots in the Shootout and will start the race from ninth, while Jack Le Brocq struggled for tyre temp open his lap an ended up 10th.
The Supercars field will take part in a warm-up at 10:10am before the Sandown 500 kicks off at 2:15pm.
