New Zealand owed seasoned goalkeeper Kyle Pontifex a debt, for some sterling work in the half, while Kane Russell and Ryan Archibald were prominent figures in an often-desperate defensive operation.
Attacker Nick Wilson did have the ball in the Australian net in a rare attacking foray, but it was ruled out for an earlier infringement.
However New Zealand were chasing the game for most of the half as Australia, last beaten by the Black Sticks in the final of this tournament a year ago, tightened the screw.
However the second half was a different story. New Zealand were more assertive and did create chances.
They found space to attack down the right in particular, with Russell prominent, and from that flank came New Zealand's best chance.
Russell made good ground in from the right, got the ball back to an unmarked Hugo Inglis, who swivelled and slapped his shot inches wide of an open goal.
Replacement goalkeeper Devon Manchester made an important block from Flynn Ogilvie but New Zealand gained traction through the half.
The shots and circle penetrations favoured New Zealand in the third quarter and they managed five penalty corners overall but were unable to find a way past Australia's classy goalkeeper Tyler Lovell.
Australia sit top of the standings, unbeaten with 12 points from four games.
New Zealand have eight points from five, while India are shaping as their rivals to make the final. They have six points from three games before their match against fierce rivals Pakistan tonight.
World No 7 India and New Zealand meet on Wednesday night before New Zealand have a bye. That match is expected to decide the second finalist for next Sunday night.
