Defending only 196, the Australian attack kept New Zealand batters under a tight leash with great line and length in helpful conditions for bowling, eventually skittling the visitors out for just 82 in 33 overs.
The early damage to New Zealand was caused by seamer Sean Abbott, who came into the side after all-rounder Cameron Green was ruled out due to the cramps he suffered during his match-winning effort in the first ODI.
After Mitchell Starc dismissed Martin Guptill in the opening over of the innings, Abbott sent back Devon Conway and Tom Latham in his first over and conceded only a single run in his spell of five overs.
New Zealand were reduced to 14-3 and their hopes depended heavily on captain Kane Williamson but he was out cheaply, trapped leg before wicket off a full toss delivery from Zampa.