Having opted to bat first, the home side were dismissed for 248 after 48.1 overs. In reply captain Suzie Bates made an unbeaten 122 to lead her side to victory after 44.5 overs.
Runs flowed from the get go in the White Ferns pursuit, with the wicket of Lucy Doolan for 10 the only blemish in an otherwise strong start.
Amy Satterthwaite joined her skipper and was aggressive against the Australia bowling attack early. The pair kept on top of the required run-rate and held the momentum for much of the innings.
Both players brought up their half-centuries in quick succession and took New Zealand to 152 for one after 28 overs.
Satterthwaite was eventually dismissed lbw on 98, with New Zealand on 196 after 36 overs. The innings featured 16 boundaries and came off just 95 balls.
Bates though remained at the crease and brought up a brilliant century four overs later to claim her third career ODI ton. She then capped off the inspirational knock by seeing out the match with Sara McGlashan (17*) to wrap up an emphatic victory.
Bates's Player of the Match performance was highlighted by 16 fours and a six and came off 131 balls.
Earlier, the Stars had come back from a mid-order collapse to post a competitive total.
Meg Lanning was the anchor in the Australian innings, scoring 87 from 71 balls, but lost wickets around her regularly. Rachel Candy took two key wickets early on to help reduce Australia to 148 for five.
Lanning's innings was then cut short soon after when she was run-out at the bowlers end, having slipped while backing-up.
An eight wicket partnership worth 80 between Jodie Fields (51) and Rachael Hayne (34) somewhat revived the Australian innings, taking them to 237 for seven.
Candy though struck twice more at the end of the innings to limit Australia to two short of 250.
The 26 year-old finished with figures of four for 36 from nine overs and found help from Sian Ruck and Morna Nielsen who picked up two wickets apiece.
New Zealand now leads the four match series one-nil, with the second match to be played on Friday.
