They chased 350 to win 3-0 at Hamilton in 2006-07.
The Australian top and middle orders established three separate platforms to launch a winning chase but could not convert.
They lost their first two wickets - Shaun Marsh and Peter Handscomb - on 44 in the eighth over; their next two - Aaron Finch and Glenn Maxwell - fell six balls apart in the 21st and 22nd; and batsmen five and six - Travis Head and James Faulkner - exited on 173 and 174 in the 33rd.
Santner then produced the coup de grace, luring Stoinis into a lofted drive on 42 off 48 balls. Jimmy Neesham loomed as the ball swirled at long on and took a catch in the face of the setting sun.
An eighth-wicket stand of 51 runs between Pat Cummins and Mitchell Starc brought Australia back but, needing 33 off as many balls, Cummins heaved a catch to Santner at mid-wicket.
Such catches were a highlight of the Black Caps' display with Dean Brownlie and Boult displaying safe hands and cool heads within the vicinity of the boundary to remove Finch (56 off 64) and Head (53 off 72). Latham's take of Maxwell, standing up to Santner, and Taylor's first slip scoops of Faulkner and Adam Zampa further highlighted their skills.
A couple of caught-and-bowleds to Tim Southee and Kane Williamson were dropped, but you'd need to be filming The Matrix bullet dodge scene to catch them.
New Zealand hummed early, but missed the opportunity to reach full throttle.
The hosts reached 281 for nine, led by Taylor's 16th ODI century which equalled Nathan Astle's New Zealand record in the format. The No.4 finished with 107 off 101 balls.
Taylor was savage in the early stanzas before consolidating through the middle as crucial wickets were lost. That included 29 consecutive singles from 36 balls rotating the strike at will between 68 and 97. He milked 75 of his runs in an arc between gully and cover.
Taylor looked so relaxed on the Patumahoe clay that he might as well have ventured out with a beach towel. The right-hander has scored 40 or more in six out of seven innings across all formats since recovering from surgery to remove a pterygium off his left eye late last year.
New Zealand stumbled between the 32nd and 41st overs, losing four wickets for 33 runs. The innings threatened to unravel despite sound partnerships for the second and third wickets.
Brownlie, playing his first ODI since December 2014, anchored the innings with 63 from 78 balls, including a 100-run partnership off 102 balls for the third wicket with Taylor and 70 for the second wicket with Williamson (37).
Brownlie flayed the tourists early, reaching 27 from as many balls, before compiling 25 consecutive singles off 45 deliveries. James Faulkner, a master of the slower ball, had the opener swing at a delivery which struggled to carry to wicketkeeper Peter Handscomb. Initially Brownlie was given not out in the confusion, as the bat hit the ground. A review forced his exit.
Faulkner also took the pace off to remove Broom, who nibbled off the back foot. Josh Hazlewood reinforced Faulkner's work by getting Colin Munro to force a drive to Starc at mid-off and Jimmy Neesham to chop on.
Faulkner (10-0-59-3) pipped Starc (10-1-63-3) for the honour of best visitor bowling figures, despite the latter bowling Southee and Lockie Ferguson with consecutive balls in the final over. Santner made 38 not out off 34 deliveries, including two fours and a six to finish.
In a marked contrast to the waterlogged McLean Park on Thursday, Waikato sunshine beamed across the ground on a fair ODI wicket.
