Victory's hero from the last round, 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 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, 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, with Troisi scoring the equaliser deep into injury time, and they seemed to pick up where they had 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 New Zealander's feet.
Victory dominated the early stages but barely tested Theo in Brisbane's goal apart from that early chance.
But they 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 byline.
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 Nathan 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.
