Lynn (44 runs from 33 balls) and Maxwell (40 not out from 24 balls) shared in a scorching 77-run stand from just 53 balls to steer Australia to the rain-reduced total of 95 from 15 overs with 21 balls to spare.
Despite a top-order wobble, in which captain David Warner and the debutant D'Arcy Short fell inside the first three overs, the belligerent power of Lynn and Maxwell swamped the Kiwi bowling attack.
Stanlake startled Colin Munro with his high bounce for debutant wicketkeeper Alex Carey to race out to point to complete the catch.
Martin Guptill was then flummoxed next ball by a perfect-length seamer that flicked the top of off stump.
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Stanlake narrowly missed his hat-trick as Tom Bruce clipped an attempted yorker through the leg side for three.
Tye mopped up the Kiwi tail to finish with four wickets for 23, while towering paceman Stanlake claimed three wickets inside the powerplay to dismantle the Kiwis' top order.
Australia had New Zealand at 60 for five before Colin de Grandhomme hit an unbeaten 38 from 24 balls with three sixes and a four.
De Grandhomme launched two massive sixes off leg-spinner Adam Zampa with the Black Caps managing just four sixes in the entire innings.
Stanlake underlined why he is one of the hottest prospects in the country and has been locked up on a Cricket Australia central contract.
Australia play England in the second match of the tri- series in Hobart on Wednesday.