Their superior class and cohesion was reflected in 58 per cent possession and 20 shots, with nine on target (New Zealand had five and two respectively).
Mexico will wonder how they didn't score more goals but a combination of poor finishing, strong goalkeeping and stout defending kept them at bay.
The Ferns showed some glimpses on attack, but will need to demonstrate more ambition.
But the most important outcome was to avoid defeat, which gives them an early foundation in the tournament and some confidence.
It's a quick turnaround for New Zealand, who face Germany on Sunday (5am), with the Europeans falling to a late Colombian goal in the other group B match (1-0).
On Thursday the Ferns had an early chance, with Ava Pritchard caught on her heels as a dangerous cross from Milly Clegg flashed across the six yard box.
That was as good as it got though, as Mexico soon took the initiative with their neat passing game.
The Ferns mostly dealt well with the pressure – with captain Kate Taylor always where she needed to be in central defence – though struggled to get their counter attacking game going, with simple passes missing the mark.
Mexico should have gone ahead in the 22nd minute, but Taylor blocked the route to goal when the ball fell to the feet of Alexxandra Ramirez.
The Ferns were also fortunate when a long range free kick evaded everyone, including keeper Sheaff, but also drifted wide of the far post.
In the 31st minute, completely against the run of play, New Zealand took the lead.
Wisnewski regained possession near halfway, then broke forward. With options either side, Wisnewski opted for a long range shot, which took a big deflection off Carol Cazares to catch out the goalkeeper.
It was a lucky break, though also reward for Wisnewski's assertive approach.
The goal was the catalyst for New Zealand's best period. They enjoyed some spells of possession, with Alyssa Whinham and Clegg prominent.
Unfortunately, the Junior Football Ferns went to sleep just before halftime. On the balance of play Mexico's equaliser was deserved, but the manner of the concession was disappointing.
New Zealand failed to clear a looping pass, before a cross eventually found its way to Anette Vazquez, who tucked her shot into the far corner, despite the presence of several defenders.
Just after the hour Alyssa Whinham found Clegg with a delightful slide rule pass, but her scuffed attempt was covered well.
A wonderful point blank save in the 71st minute from Sheaff kept New Zealand on level terms, as the Ferns began to retreat further and further into their own territory.
Mexico should have taken the lead a few minutes later, but the unmarked Natalia Mauleon skied her attempt from 10 yards.
There were further half chances but the Ferns held on to their precious point.
New Zealand 1 (C Cazares own goal 31')
Mexico 1 (Anette Vazquez 45')
Halftime 1-1
Live updates of the U20 Women's World Cup clash between New Zealand and Mexico.
