Netherlands edge Australia in five goal thriller.
Tim Cahill earlier cancelled out Robben’s opener with one of the greatest goals in World Cup history before a controversial penalty from Mile Jedinak nine minutes after the restart had Ange Postecoglou’s men dreaming of a famous upset.
However, Van Persie quickly leveled things up in the 58th minute with a neat finish inside the area.
And Memphis Depay who had come on as a substitute for the injured Bruno Martins Indi broke Australian hearts with a speculative effort that goalkeeper Mat Ryan will feel he should have kept out.
The Oranje can now become the first team to qualify for the round of 16 if Group B’s other match on Wednesday between holders Spain and Chile ends in victory for the latter or a draw. Australia, meanwhile, face a near impossible task to progress having lost both group games.
Robben’s third goal of the tournament in the 20th minute ensured things livened up into life after a lacklustre opening.
The winger escaped the attention of Alex Wilkinson on the halfway line and surged into the box before drilling a low, angled shot into the bottom right-hand corner.
Just less than 60 seconds later, Cahill equalised with a wonderful strike which the Australians would savour for a long time to come.
Ryan McGowan who played at right-back in the absence of injured Ivan Franjic drilled a superb cross-field pass towards Cahill, who watched the ball over his shoulder and lashed an unstoppable left-foot volley that crashed past the helpless Jasper Cillessen and struck the crossbar before nestling in the net.
It could have been even better for Australia on the half-hour mark, Mathew Leckie fizzed a ball across the area, but the onrushing Mark Bresciano could only side-foot over the bar.
The half ended on a sour note for the Netherlands when Martins Indi was carried off the pitch on a stretcher after a poorly timed challenge from Cahill, who received a booking that means he misses Australia’s final group game with Spain.
Things got worse for Netherlands after the break.Van Persie was first cautioned for an elbow on Matthew Spiranovic that rules him out of the last pool game with Chile before Jedinak put Australia ahead from the spot in 54th minute.
However, four minutes later, the Netherlands levelled up again.
Wesley Sneijder’s intricate throughball was received by Van Persie and the Manchester United striker turned well in the area before rifling a shot into the roof of the net for his 11th goal in his last 10 international appearances.
And, with just over 20 minutes remaining, the Dutch comeback was complete.
Van Persie’s clever run saw the pitch open up for Depay and his speculative effort from 25-yards found its way home via a costly error from Ryan.
Australia pushed forward in the closing stages in desperate search of an equaliser, but the Netherlands easily dealt with the danger to all but secure their place in the last 16.