In a sensational opening half the Socceroos not only matched it with their highly-rated opponents but dominated, enjoying 51 per cent possession.
It wasn't long before Robben's blinding pace exposed the Socceroos back line as he tore his way from the halfway line past centrebacks Alex Wilkinson and Matthew Spiranovic to put the Dutch 1-0 ahead in the 19th minute.
But just as he did in Australia's opening match against Chile, Cahill replied for the Socceroos.
The veteran striker got on the end of Ryan McGowan's ball to strike a blistering volley and level things up in the 21st minute, his fifth World Cup goal sure to feature on highlight reels for years to come.
From there Australia kept the momentum and started dominating the match, creating havoc for the Dutch defence.
Fellow veteran Mark Bresciano could have given Australia the lead after Mathew Leckie provided the perfect cross into the box but he sent it over the crossbar.
The chances kept coming for Australia with Spiranovic getting in on the action but the defender was unable to make it count.
Cahill drew the first yellow card of the match just before halftime, clattering into Dutch defender Bruno Martins Indi who needed to be stretched off and replaced by Depay.
Having incurred a yellow card against Chile the striker will now miss Australia's clash with Spain.
Van Persie will also miss the Netherlands' last group clash against Chile, having copped a second yellow card in two matches for a foul on Spiranovic.
The Socceroos began the second half with just as much gusto, taking the game to the Dutch.
Bresciano was replaced by Oliver Bozanic and it didn't take long for the midfielder to have an impact.
Playing the ball into the box it deflected off Daryl Janmaat's arm with the Socceroos awarded a penalty for handball.
Jedinak stepped up to the mark and made no mistake to give Australia the 2-1 lead in the 54th minute.
Celebrations were short lived as the Socceroos' defence was again exposed by an unmarked van Persie, who drew things level.
The Dutch found the winner after substitute Depay fired a long-range strike from 30 metres in the 68th minute.
-AAP
- AP