
Set 187 to win after bowling the Kiwis out in the first session on day three, the hosts were made to work hard for every run.
Trent Boult took 5 for 60 but Shaun Marsh's 49 and 28 each from Adam Voges and Mitchell Marsh proved decisive.
Josh Hazlewood took a career-best 6 for 70 to help dismiss New Zealand for 208.