The veteran midfielder scored just 17 minutes after being introduced from the bench, heading home Tommy Oar's 69th-minute corner with the help of a notable deflection at Sydney's Allianz Stadium.
It allowed Postecoglou, who replaced Holger Osieck after a 6-0 loss to France, to mark the occasion of his first match in charge with a promising victory.
After Milligan had set up Mathew Leckie to shoot wide, Kruse's heavy touch let him down after he had been sent clear by Rhys Williams' excellent throughball.
Postecoglou's men continued to probe, earning a corner from which Mile Jedinak fired a shot on goal from inside the six-yard box, but Pemberton made a comfortable save.
Cahill was brought on in the 52nd minute, replacing Leckie, and he rose highest to nod in Oar's excellent delivery, with the ball taking a wicked deflection off Junior Diaz on its way in.
