Cathryn Finlayson scored the only goal of the game in the third minute when she swept home a penalty corner rebound from virtually the Blacksticks' first attack.
They continued to dominate possession but Australia created the better chances after that and could have at least been level by half-time.
Georgia Nanscawen could have equalised from four yards at the far post but allowed the ball to hit her foot before she poked home.
Then, in the 14th minute, Megan Rivers smashed a shot against goalkeeper Bianca Russell's right hand post but ball rebounded across face of goal and out for a sideline hit.
Australia did not win their first penalty corner until seven minutes before the break but Anna Flanagan's low drag flick was saved low to her right by Russell.
Early in the second half New Zealand's Charlotte Harrison and Gemma Flynn both had efforts saved by Toni Cronk but as they sat back to break on the counter-attack Australia began to press for the equaliser.
Both teams lost players to the sin-bin but neither could take advantage of their numerical advantage and even the Hockeyroo's decision late on to replace Cronk with a kicking-back failed to pay off as New Zealand hung on to win the opening game of the tournament.
Early on Belgium goalkeeper Aisling D'Hooghe looked like keeping the Dutch at bay with a string of saves but once her goal was breached by Lammers, who by a quirk of selection and injury made her bow in the Games despite her international debut coming in 2003, just before half-time there was only going to be one winner.
The 31-year-old cleverly deflected Eva de Goede's 40-yard pass into the circle to beat D'Hooghe before coolly converting her second after the break following a good run to the right byline by Ellen Hoog.
Ten minutes from time, Caia van Maasakker converted a deflected penalty corner for the third.