Busy attacker Kelsey Smith, named player of the match, was involved on the left side of Australia's defensive circle and when the ball fell to Merry she picked her spot to score at the near post from a difficult angle.
Australia bounced back smartly, Emily Smith making it a 26th birthday to savour when she capitalised on a defensive blunder, which had goalkeeper Sally Rutherford well out of position, to roll the ball into an empty net.
The first half was pretty even and New Zealand would have regained the lead when Sam Harrison slapped a reverse stick shot into the Australian goal.
But it was ruled out on an Australian referral as it came off the back of her stick.
Australia were stronger in the third quarter and there were trying defensive situations for New Zealand, in which Neal was outstanding, and Liz Thompson and Ella Gunson also key figures.
Going forward captain Stacey Michelsen's weaving runs were top class and troubled Australia's defence while Smith, Sam Charlton and Merry also proved a handful. But New Zealand needed more out of world class midfielder Anita McLaren who was below her best.
Merry had one great opportunity, made by her own skill in the penalty area, gathering a cross and turning well to get a shot in but Australia's goalkeeper Rachel Lynch was up to the job.
Both teams had six penalty corners but the defensive units were up to the job, Neal blocking one Jodie Kenny drive with her stick.
Belgium thumped Japan 6-3 to go second in the group. They will face Spain in the other crossover game.
New Zealand will play world No 3 Argentina on Tuesday morning (NZT).
New Zealand beat them in the world league final in Auckland late last year but lost four and won only one of their matches on a tour to Argentina in February.
In a quirk of the draw, if New Zealand beat Argentina, they will face Australia again in the quarter-finals.
