Mile Jedinak's penalty and a brace from Tim Cahill, who, playing at his old Millwall stomping ground of The Den, broke Damian Mori's record to become Australia's all-time leading goal-scorer, appeared to put Postecoglou's team into a comfortable position.
Ecuador, though, came out after the break looking more like the team that finished fourth in CONMEBOL World Cup qualifying, capitalising on Mitchell Langerak's red card to register an unlikely comeback victory.
Goals from Fidel Martinez, Segundo Castillo and Enner Valencia hauled Ecuador level at 3-3 with 13 minutes remaining before substitute Edison Mendez claimed an injury-time winner.
Cahill opened the scoring with eight minutes played.
Mark Milligan headed Tommy Oar's corner back into the danger zone and Cahill was on hand to nod it home and enter the record books.
Australia were awarded a penalty in the 16th minute when Cahill went down after grappling with Gabriel Achilier inside the area and Jedinak stepped up to slot home the resulting spot-kick with ease.
It was 3-0 after 32 minutes.
A quick break near the half-way line allowed Mathew Leckie to advance and swing in a cross, which Cahill dived to connect with and head past Adrian Bone in the Ecuador goal.
Seven minutes after the restart, Martinez prodded the ball home after being found in a dangerous area by Enner Valencia's pass.
Ecuador had a second less than 60 seconds later and Australia found themselves down to 10 men.
Langerak rushed out to try and clear a ball into the area but Valencia got there first and the Borussia Dortmund goalkeeper was shown a straight red card after sending the Ecuador forward flying into the air.
Castillo made it 3-2 from the penalty spot and the sides were level when Antonio Valencia advanced into the area and cut the ball back for namesake Enner Valencia to guide past Brad Jones - Australia's third goalkeeper of the match after Mat Ryan had played the first half.
With the clock ticking down it looked as if Australia would survive to claim a draw but an error from Alex Wilkinson, who was dispossessed in a dangerous area, allowed substitute Mendez to net in the 92nd minute.
