New Zealand striker Amber Hearn rifled home the match winner in the 35th minute, perfectly placing a right-footed drive into the corner of the net from the edge of the penalty area, after a free-kick was played into her path by Rosie White.
From there the Kiwis dug deep with a strong effort both in and out of possession with goalkeeper Nayler also playing a key role, denying Brazil's Cristiane mid-way through the second half with a superb save one-on-one.
The result is the second win for the 16th ranked Football Ferns over Brazil (7), the first coming in Switzerland in 2013 at the Valais Cup - also a 1-0 win provided by a Hearn goal.
"I can't really put into words how important Amber is to the team, she's incredibly important on the pitch and off the pitch and she works incredibly hard," said Readings. "It's nice to see her get the rewards because she works so selflessly for the team but today she also showed her quality in front of goal."
The Ferns meet Brazil again on Wednesday in the second match of their two-game series, aimed at giving the squad valuable experience playing in the conditions they will face if they qualify for next year's Rio Olympics. New Zealand must beat Papua New Guinea in a qualifier in January to secure their berth at the games.
"It was very, very hot today and the conditions are likely going to be even trickier for our next game. There's not much of a chance for recovery in the turn around, but if we can be better in the next game that's another step forward in our Olympic preparation. And that's what we need every game. We're together very rarely and we can't waste an opportunity, and we didn't today."
Brazil 0-1 Football Ferns (half: 0-1)
BRA: -
NZL: Amber Hearn 35'