It was all green and gold from the opening hit in Sydney, with Wickham making the most of a lung-busting run from Matthew Swann in just the second minute.
The lead doubled when Wotherspoon turned two defenders to score three minutes later.
Whetton continued Australia's dominance with a goal after quarter time, before Zalewski added a fourth off a neatly-executed Tom Craig cross in the 19th minute.
Not even a green card against Joshua Beltz could swing the momentum in New Zealand's favour, with Australia taking a comfortable 4-0 lead into halftime.
The third quarter fell into a deep lull with neither team sustaining any pressure until Zalewski completed his double off a third consecutive penalty corner to end the period.
Wickham then completed the win with his second deep into the fourth quarter.