The New York Red Bulls star soared to match Damian Mori's 29-goal tally for his country on 69 minutes to give the Socceroos a deserved victory in front of a 20,165 strong crowd on Tuesday night.
The goal had been coming for a while as Australia sought to impose Postecoglou's attacking ideals as he took charge for the first time in what promises to be a bold new era.
Postecoglou showed he wasn't afraid to experiment by leaving Socceroos talisman Cahill on the bench, and handing a first full start to German-based striker Mathew Leckie, who began brightly using his electric pace to harass the Costa Rica defence.
But, in the end, it took a trademark Cahill intervention to settle the issue.
Brisbane's Ivan Franjic and Jason Davidson were named as the fullbacks, with Middlesbrough's Rhys Williams partnering Lucas Neill at the heart of the defence and Club Brugge gloveman Mat Ryan getting the nod ahead of Mitch Langerak in goal.
Mark Bresciano - facing a four month FIFA ban for transfer irregularities - was handed a playmaking role with Leckie receiving support from Dario Vidosic on the left and Robbie Kruse on the right.
The holding midfield spots went to Mile Jedinak and Mark Milligan.
After a nervous start Australia showed plenty of enterprise with Kruse wasting a chance to burst through on goal alone after he failed to take control of an incisive through ball from Williams.
At the other end, Australia had an escape in the fourth minute when Davidson - who scored an own goal on his debut against Scotland last year - got in a mix up with Ryan, his header under pressure from Ticos attacker Joel Campbell forced Franjic to clear off the line.
Leckie, who scored in last month's 3-0 win over Canada, should have hit the net again in the 42nd minute - but he snatched at an inviting cross from Kruse, sending the ball flying over the crossbar with the goal at his mercy.
Playing with verve and good movement, Australia was full of purpose against a Costa Rica side ranked 26 places above it in the FIFA rankings.
Postecoglou made his first chance in the 47th minute, replacing Williams - who came into the game carrying a knock - with Shandong Luneng's Ryan McGowan.
Australia showed its purpose had not wavered in the second half, with Cahill also introduced into the fray in place of Leckie and then Jedinak riding a challenge to fire just wide from the edge of the area.
In a bid to find a breakthrough, Postecoglou introduced Celtic's Tom Rogic and FC Utrecht's Tommy Oar in place of Vidosic and Bresciano on the hour mark.
Rogic, who was all class and composure, make an immediate impact, breezing past a couple of challenged before being crudely felled 25 metres out, with keeper Patrick Pemberton saving Jedinak's free kick.
But he could do nothing to thwart substitute Cahill in the 69th minute as his downward header from a corner took a deflection on its way into the net to break the stalemate.
Postecoglou praised his side and hoped the win gave the players some much-needed belief.
"I couldn't fault the players' endeavour and their willingness to embrace what we're trying to do - they were fantastic," he said.
"It was our first time together and we're trying to adjust how we do things, so full credit to them and that goal gives them that reward and hopefully some belief moving forward."
Wellington Phoenix's Carlos Hernandez and Kenny Cunningham came on as second-half substitutes for Costa Rican, which was were largely left wanting in most aspects of the game - with a handful of regulars not making the trip to Australia.