New Zealand, which beat India by 47 runs in its first game, restricted Austrlalia to 134-9 in reply to 142-8.McClenaghan finished with 3-17 and Santner 2-30 as Australia was left to get 19 runs off the last over from Corey Anderson.
Earlier, left-arm pace bowler James Faulkner and offspinner Glenn Maxwell returned identical figures of 2-18 after New Zealand opted to bat first on a slow pitch.
Opener Martin Guptill struck 39 off 27 balls with two fours and four sixes, and captain Williamson made 24.
Grant Elliott (27) and Colin Munro (23) chipped in with useful efforts.
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