Australia's new boss ended his tenure as Victory coach on a winning note thanks to Troisi's stunning second-half effort
Victory's hero from last week, James Troisi, again made the difference, scoring the only goal of the contest 11 minutes after half-time when he out-sprinted Brisbane captain Matt Smith and then slid the ball into the net from the tightest of angles.
Troisi's fine finish clinched Melbourne's first win of the 2013/14 A-League season but they had to survive a nervous finish on Friday night as Postecoglou's former club Brisbane pushed hard for an equaliser.
In Postecoglou's 32nd and final match in charge of Victory, the Roar had enough chances to score at least one goal but were unable to spoil the party for the coach who led them to back-to-back championships.
The win takes Victory to second in the A-League with five points, just behind Brisbane (six points), although the eight other clubs have yet to play in Round Three.
Victory had finished last week's clash with Adelaide United full of running as they came from behind to clinch a 2-2 draw and seemed to pick up where they left off at Etihad Stadium.
In just the third minute, the hosts' pressing saw them win the ball on the halfway line, before Mitch Nichols played a pass in behind to Kosta Barbarouses, who stormed in from the right only for Michael Theo to save at the Kiwi's feet.
Victory dominated the early stages but barely tested Theo in Brisbane's goal apart from that early chance.
After half an hour, the Roar had yet to register a shot but took control in the final five minutes before the break, with Liam Miller's header looping over the bar, before Kwame Yeboah and Jack Hingert both hit shots straight at Nathan Coe.
The home side responded after half-time and finally notched the goal their play had deserved in the 56th minute after a move down the left.
Nichols played the ball inside to Archie Thompson, who fed Troisi and the on-loan attacker burst past Smith and scored, despite shooting from up against the by-line.
While Troisi had scored the equaliser away to Adelaide in Round Two, his goal against the Roar capped off a much better all-round performance from the 25-year-old, who he began to show a better understanding with Nichols in midfield.
Victory had two big chances to double their lead soon after, with Barbarouses almost stealing the ball off Theo, while the Brisbane goalkeeper had to be at his best to deny Nichols' curling effort on the hour mark.
Ivan Franjic then tested Coe from outside the box before Barbarouses fed Thompson, who failed to lift the ball over an onrushing Theo.
As the second half wore on, Brisbane began to gain more control of the match but were unable to breach Melbourne's defence, with Thomas Broich blasting over late on, as the hosts ensured Postecoglou would leave them in victorious fashion.