Sam Kerr grabbed a first-half brace and eschewed several chances to complete her hat-trick, with her class apparent throughout.
Aside from her goal, Wilkinson went close early, directing her shot just past the far post in the fourth minute.
The Ferns generally struggled to maintain quality possession, though came into the match more after Australia made five replacements on the hour mark.
New Zealand's first half was disrupted by the loss of Paige Satchell in the 18th minute, with the winger leaving the field in some distress, related to problems with an irregular heartbeat.
Nayler was a surprise choice in goal, after Victoria Esson's outstanding performance on Friday, with Meikayla Moore replacing the injured Ria Percival in the only other change to the starting XI.
It's the second time in recent months that Esson has been demoted after a heroic display, though coach Jitka Klimkova said Nayler had earned another opportunity through strong club form.
Australia took a deserved lead in the 15th minute through Kerr. There had been warning signs for the Ferns, and the Chelsea striker scored with a powerful header from six yards, after a needless corner was conceded.
Barely 90 seconds later the Matildas went further ahead, with Hayley Raso placing her shot superbly just inside the post.
Raso had been the recipient of a favourable rebound to set up the opportunity but was still left in too much space.
Satchell departed soon afterwards, replaced by Gabi Rennie. Australia had several prime opportunities, as the Ferns struggled to get any kind of foothold.
It was no surprise when the Matildas went further ahead, through a delightful Kerr finish, tucking it past the onrushing Nayler with the outside of the foot, after springing the offside trap.
There were ominous signs for the Ferns – as Australia threatened to run up a huge score – but they were wasteful, while Nayler made a couple of timely interventions.
In that context, New Zealand's goal was a relief as well as boost, with Wilkinson finishing at the second attempt past Lydia Williams.
Similar to the South Korea series, Olivia Chance was the creator, with a delightful threaded ball and Wilkinson's strength and perseverance did the rest, poking home from six yards after her first shot had been blocked.
Kerr looked set to complete her hat-trick in the second half, but it wasn't to be. She twice headed wide from promising positions, while Ali Riley and Meikayla Moore managed timely blocks against the Chelsea striker. Caitlin Foord also hit the crossbar with Nayler well beaten.
New Zealand enjoyed some periods of possession - without threatening to score – while Australia lost their edge with the wholesale changes, as the sting went out of the match in the final 20 minutes.
Football Ferns 1 (Hannah Wilkinson 45+3)
Australia 3 (Sam Kerr 15, 32 Hayley Raso 17)
Halftime: 1-3
