Things almost got even worse with Tyler Bindon sent off, before the decison was changed to a yellow card after a VAR review.
Bazeley made two alterations from Canberra, with Finn Surman (for Michael Boxall) and Ben Old (Callum McCowatt) brought in.
For his part Australian coach Tony Popovic made six changes, with Toure and Nestory Irankunda among those introduced.
For the second match in succession, the All Whites made the more assertive start. There were a series of half chances, as they tried to push down both flanks, with Sarpreet Singh and Ben Old prominent. A snappy one touch move just before the half hour was the highlight, as quick exchanges eventually fell to Wood, who directed his sidefooted effort too close to Izzo.
Australia had started to warm to their task and find space in the final third, before their breakthrough 10 minutes before halftime. It came through the heart of midfield. After a quick turnover, Connor Metcalfe threaded a pass for Toure, who shrugged off Tyler Bindon before a composed finish past Crocombe.
Just like in Canberra it was preventable, as Bindon was probably favourite to win the ball but appeared to slip. The All Whites had narrowly escaped danger minutes away, with a brilliant Crocombe save to claw away a Kye Rowles header, after Australia attacked down the right.
The All Whites should have equalised in the 39th minute, but Payne failed to connect with his angled header, with the goal open. It was a neat flowing move, as Singh escaped down the left, before his deflected cross was brilliantly tipped onto the cross bar by Izzo, with Payne unable to bury the rebound, albeit at an awkward height.
New Zealand started well after the break. An Old cross just eluded two teammates, while Thomas forced a great save from Izzo, after a turn and left footed half volley, a neat piece of skill from the Dutch based player. But the All Whites were undone by a long range break, with Irankunda outwitting both De Vries and Bindon, before finishing on the angle past Crocombe.
That stunned the crowd, before Wood finally got his moment. It was a clever finish, as he latched onto De Vries’ through ball, then stretched to get a touch past Izzo. That prompted a massive cheer but all that momentum was undone by another Australian goal.
This time it was Toure creating havoc, as he was released by Metcalfe, before standing up Surman and squeezing it past Crocombe. The crowd was in shock and there was almost more disaster, as Toure got through again to finish – with a simple one-two in the area – but it scratched for offside.
Still, it was a bad sign, as the rest of the team wondered what was happening at the back. Bazeley removed his ‘big three’ just after the hour mark (Wood, Thomas and Old) for Jesse Randall, McCowatt and Callan Elliott.
A flashpoint came in the 71st minute with Bindon shown a straight red card, as he lunged in on Irakanda. It looked a harsh call – as the New Zealand coaching staff remonstrated with the fourth official, before referee Don Robertson reveretd to a yellow card following a VAR check.
Irankunda was unlucky with a spectacular 35 metre free kick, as it hit the cross bar and bounced out, with Crocombe well beaten.Luke Brooke-Smith injected some energy in the last 15 minutes, as the All Whites tried to find a late highlight.
All Whites 1 (Chris Wood 57)
Socceroos 3 (Mohamed Toure 35, 60, Nestory Irankunda 54’)
Halftime: 1-0