The match sprang to life in the 56th minute when recruit James Troisi scored his second goal in as many games.
It was a strike to gladden the heart of the new Australian coach, with Troisi hitting the target with a curling shot from a tight angle after fine lead-up work by two other men who have represented the Socceroos - Mitch Nichols and Archie Thompson.
Nichols could have doubled the Victory's advantage only four minutes later, but his powerful strike was brilliantly tipped over the bar by Roar keeper Michael Theo.
Thompson also had a shot blocked by former Victory teammate Theo shortly afterwards, while Ivan Franjic forced a diving save out of Melbourne keeper Nathan Coe at the other end in the most frenetic period of the match.
Brisbane's star German midfielder Thomas Broich had a late chance to give his team a share of the points, but his snap shot in injury time flew over the crossbar.
It was the Victory's first win of the season and their first success over the Roar in more than three years.
Brisbane were the only team to have started the 2013-14 season with successive victories but struggled to make an impact in the final third of the pitch on Friday night in the absence of injured striker Besart Berisha, who picked up a hamstring strain early in last weekend's 4-0 rout of Sydney FC.
The home side started the stronger on Friday night before a crowd of 21,693 at Etihad Stadium.
Troisi and Nichols were involved in most of the Victory's better first-half attacking moves, although they rarely looked like troubling Theo.
But the Roar dominated the last 20 minutes of the first half, with the best chance falling to Jack Hingert, whose powerful strike was parried away by Coe.
Postecoglou won back-to-back A-League titles with the Roar before joining the Victory for the 2012-13 campaign.
He starts his new job as Australian coach on Saturday, with his first match in charge of the Socceroos a friendly international against Costa Rica in Sydney on November 19.
Kevin Muscat is the red-hot favourite to succeed Postecoglou as Victory coach in time for their next game against Wellington Phoenix on November 4.
The Roar return to Suncorp Stadium to host Melbourne Heart on November 3.