The game took a dramatic turn in the 21st minute when Australia bounced back draw level with the Dutch who had gone ahead in the preceding minute of the match.
Tim Cahill, Australia's highest goal-scorer, brought his team back into a do-or-die contest against a confident Netherlands side which beat defenders Spain 5-1 in their first match last week.
Robben scored in the 20th minute to give the Netherlands the short-lived lead. This was his third goal in this World Cup.
The scoreline remained 1-1 at half-time. The bad news for Australia was that Cahill was shown the yellow card, his second successive one, which meant that he would the crucial tie against reigning champions Spain on June 23.
This is the first time that these two teams are playing in the World Cup finals.
Nine minutes into the second half, Algerian referee Djamel Haimoudi gits a spot kick to Australia after the Netherlands' Janmaat handled a ball inside the box. Captain and midfielder Mile Janidek put Australia 2-1 ahead in the 54th minute.
van Persie scored his 17th goal for the Netherlands in the tenure of coach Gaal
But the Australian joy didn't last long as Manchester United forward Robin van Persie made it 2-2 in the 58th minute. This was Persie's third goal of the tournament and 17th of his team's 56 scored in the two-year tenure of current coach Luis van Gaal.
The Netherlands took a lead for the second time in the match when Memphis Depay received the ball on the turn and smashed it home from around 25 yards out. This was Depay's first goal for the Netherlands.
Robin van Persie was substituted in the 88th minute of the match and he handed over the captaincy to Robben.