Boult finished with 4-51 but Usman Khawaja (88) and Alex Carey (71) forged a century-plus stand to help Australia post a competitive 243-9.
Chasing 244 for victory, New Zealand were all out for 157 in the 44th over, with skipper Kane Williamson top scoring for them with 40.
Mitchell Starc (5-26) was the pick of the Australian bowlers in a one-sided rematch of the 2015 World Cup final.