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The home side, opting to bat first, were dismissed for 248 after 48.1 overs and Bates' third international century led her side to victory with 5.1 overs to spare.
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 following Doolan's departure and was aggressive against the Australian bowling attack early.
Both players brought up their half-centuries in quick succession and took New Zealand to 152-1 after 28 overs.
Satterthwaite was eventually dismissed for 98, but Bates remained at the crease and brought up a brilliant century four overs later.
Bates 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 from 131 balls.
Earlier, the Stars had come back from a middle-order collapse to post a competitive total.
Meg Lanning was the anchor in the Australian innings, scoring 87 from 71 balls, but the Stars lost wickets regularly.
An eighth-wicket partnership of 80 between Jodie Fields (51) and Rachael Hayne (34) somewhat revived the Australian innings to ensure they posted a competitive total.
White Ferns' seamer Rachel Candy finished with figures of 4-36 from nine overs, and found help from Sian Ruck and Morna Nielsen who picked up two wickets apiece.
New Zealand leads the four match series 1-0, with the second match to be played tomorrow.