"We lacked the intensity of the day before. It's difficult to get up for back-to-back matches but it was the same for New Zealand. Overall, we're pleased we managed to grind out a result."
West Australian Aran Zalewski celebrated his 50th appearance for Australia.
The match burst into action two minutes into the second quarter when Wotherspoon, 22 and celebrating his birthday, scored to give the Kookaburras the lead.
Seven minutes later, Dwyer continued his incredible run of form, scoring for the fourth consecutive match to take his tally for the tournament to seven and doubling Australia's advantage.
And defender Hayward, who made his international debut at the same tournament a year ago, made it 3-0 with a powerful penalty corner conversion, his first goal of the cup.
The Black Sticks were handed an opportunity to get back into the match two minutes after halftime when a penalty corner hit an Australian defender on the line. Hayward slotted home the resulting penalty stroke but it was to be New Zealand's only goal.
The Kiwis remain favourites to meet the Kookaburras in Sunday's final but could still lose out if the Koreans beat Malaysia and then beat the Black Sticks tomorrow.
Looking ahead to the weekend, Gaudoin said Australia would not think about Sunday's final ahead of their clash with India on Saturday (6:10pm AEST) in their fifth and final pool game.
"It's a classic case of not looking beyond the next game. India are playing reasonably well. They probably haven't had the results they've deserved here so far."
SULTAN AZLAN SHAH CUP STANDINGS:
* 1. Australia (12 points, 4 games)
* 2. New Zealand (9 points, 4 games)
* 3. Korea (4 points, 3 games)
* 4. India (4 points, 4 games)
* 5. Malaysia (3 points, 3 games)
* 6. Canada (0 points, 4 games)
- AAP
